But despite tries from Alex Grove, Andy Short and Ben Howard they came up just short in Wycombe against a spirited Wasps team that took their chances well.
The defeat was by no means a terminal blow to Worcester's chances of making the semi-finals, though, with the pool now intriguing balanced going into fixtures with London Irish and Saracens next year and Warriors remaining in top spot.
Worcester were always playing catch up from early on as prop Simon McIntyre gave the hosts the lead after capitalising on a poor lineout while the accurate Tommy Bell slotted two penalties for a slender 13-12 half-time lead.
Worcester had exploded into life with two well-worked tries in the space of two exhilarating minutes, while Wasps a man down with scrum half Jonah Holmes sin binned, as Grove and Short crashed over.
However, the boot of Bell put Wasps further ahead as the game went on before Jack Wallace's try midway through the second half looked to have ended the game as a contest.
Howard did strike back with ten minutes left but back came Wasps as Charlie Davies dived in seconds later to settle the encounter.
Worcester looked to make an impressive start to the game as Nikki Walker and Rob O'Donnell both confidently bounced off tackles to make yards while Joe Carlisle and Jonny Arr looked to play for territory before turnover ball allowed former Worcester player Hugo Southwell to crunch a huge clearing kick away.
But after a promising start, a poor lineout cost Warriors as home prop McIntyre gobbled up possession and bashed his way through a gap with Bell adding the extras from out wide to make it 7-0 to the home side.
A penalty at the scrum, as Warriors enjoyed early joy at the set piece, gave Carlisle the chance to put the visitors on the scoreboard minutes later. But his effort had the legs but not the direction as it pulled left of the posts.
It was Wasps turn to lose a lineout and Worcester countered at real pace as Jake Abbott spread the play and Errie Claassens sent Walker away into space. The big Scot raced past Tom Varndell but his kick into space was just too heavy and was touched back by Wallace for a 22 drop out.
Gillies was the next man to race into space from a lineout, but errors were hindering the Warriors as a knock-on and then penalty, for side entry at the ruck, gave Wasps ball back and the chance to attack through back row Sam Jones.
Home Number Eight Ashley Johnson was pulled up by a touch judge for a penalty that gave Carlisle a chance to shunt Warriors into the Wasps half. But the driving lineout was repelled and then Worcester came off second best at the breakdown.
Prop Ceri Jones was impressing and giving Swainston a torrid time at the scrum as the former Wales man won another penalty that Carlisle pushed close to the line.
Holmes was then sin binned after infuriating referee Rhys Thomas and Worcester looked to press home the numerical advantage.
Captain Dean Schofield and Abbott carried up close to the whitewash after a driving lineout before Carlisle flicked an intelligent reverse pass to Grove who powered his way over. Carlisle missed the conversion.
Worcester suddenly had the bit firmly between their teeth as Schofield and Richard de Carpentier carried strongly. Blair Cowan was then in the thick of the action down the wing before the ball was worked inside and, despite appeals for a knock-on, Claassens fed Short to dive in the corner.
Fly half Bell reduced the lead within three minutes with a sweetly struck long range penalty and then added another of the stroke of half-time for the lead at the break with the game delicately poised.
Warriors made one change at the break as young prop Ryan Furniss replaced Ceri Jones in the front row and O'Donnell switched sides at the scrum.
Two quick-fire penalties at the scrum then allowed Bell to extend the home lead to 16-12 with just over half an hour to play.
A lack of ball at the set piece was beginning to hurt Warriors as a stray lineout was gobbled up at the back by Johnson and Wasps went on the attack with only a superbly timed tackle from Walker stopping Varndell from dotting down in the corner.
Ben Howard and Neil Best entered the game and both were busy early on as Worcester looked for a platform to build upon as temperatures continued to tumble and bodies tired in Wycombe.
Further changes saw Andy Goode and Chris Jones come off the bench for the final 20 minutes as Warriors hunted a way back into the cup game.
Former England man Goode stepped into space immediately but just failed to find support runners with a pass out of the tackle.
Wasps inflicted a killer blow with 18 minutes left as they spread the ball wide, despite appeals for a stray lineout throw, and Wallace had too much pace and power as he slid off tackles and over.
Worcester looked to rally and succession of penalties allowed Carlisle to kick for the corner. The forwards battered up close through Abbott and Best before Arr and Goode combined with neat passes down the line to send Howard over in the corner. Carlisle cut the lead to 23-19 and the game was back on.
However, hopes of a comeback were dashed within moments as Worcester looked to play from deep and a loose kick ahead allowed the hosts to set Davies away and in the far corner to score.
Battling Worcester continued to look to play whenever possible in the dying minutes, knowing a try could secure a bonus point. But they could find no way of launching an attack from deep as Wasps secured the points on offer going into the mid-season break in the cup.
07m McIntyre t Bell c 7-0
27m Grove t 7-5
29m Short t Carlisle c 7-12
32m Bell p 10-12
38m Bell p 13-12
47m Bell p 16-12
62m Wallace t Bell c 23-12
69m Howard t Carlisle c 23-19
71m Davies t 28-19
Warriors: 01 Ceri Jones (Furniss 40), 02 Ollie Hayes, 03 Rob O'Donnell, 04 Dean Schofield (Jones 59), 05 Craig Gillies, 06 Richard de Carpentier, 07 Jake Abbott, 08 Blair Cowan (Best 50), 09 Jonny Arr, 10 Joe Carlisle, 11 Andy Short, 12 Alex Grove, 13 Jon Clarke (Howard 47), 14 Nikki Walker (Goode 59), 15 Errie Claassens
Replacements: 16 Ed Shervington, 17 Ryan Furniss, 18 James Currie, 19 Chris Jones, 20 Neil Best, 21 Paul Hodgson, 22 Andy Goode, 23 Ben Howard