John Brain vowed his Warriors would continue to fight for survival after late defeat at Gloucester - and insisted fans should be 'proud' of the Kingsholm display.
Worcester lost 33-19 at the home of the Cherry and Whites and fell seven points adrift at the foot of the table following Northampton's away victory at Leicester.
But Warriors produced a spirited and incisive performance in the derby which belied the final scoreline.
And Director of Rugby Brain insists his side will continue to play with both passion and pride until the end of the season - and can still stay up if they produce more of the same.
"This season has been the toughest of all our careers and there is no respite, but I don't think anyone who supports Worcester would be ashamed of their team after that display. They should be proud," he said.
"For a supposedly sterile attacking team we didn't look too bad, our set piece in the second half was outstanding and we scored a lovely try.
"If we play like we did against Gloucester when we meet Bath we can beat them. We've got six games left and we've got to win two more games than Northampton to stay up."
Lee Best scored Worcester's only try of the game with James Brown slotting over three penalties, a drop goal and a conversion.
But battling Warriors twice came agonisingly close to scoring other tries with Brown pulled up just short and Thinus Delport forced into touch when he thought he had scored just three minutes before the break.
"I can't remember the last time we got a break in a game," added Brain. "If we had got Thinus' try on the scoreboard I think that would have been the first one I can remember since September 2. But I'm not blaming luck for our predicament. That fact is we've lost too many games.
"It's a harsh league, margins are very fine and we have come out on the wrong side.
"It will be difficult to lift the players, because of the way the results have gone this weekend we know we are in big trouble, but we have just got to get on with it and we will keep on going."
Warriors youngsters Huw Taylor and Jack Singleton will start for England in the World Rugby Under 20 Championship final against Ireland this Saturday night at Sale Sharks' AJ Bell Stadium (kick-off 7pm).
Worcester Warriors Chief Executive Jim O'Toole has dismissed suggestions made in a national newspaper that the Club is pulling back on its long-term financial commitment to become an established Aviva Premiership Club.