But a high penalty count allowed the visitors to kick six penalties and ease to victory and a place in the last four of the competition.
"It was a big game for us - we needed a big performance after last weekend," said Hill. "We needed that springboard for next week but it didn't happen.
"We made a very sloppy start. We worked so hard on defence this week and put emphasis on it, but they walked the first try in. There were lots of missed tackles and it set the tone for the first half.
"The players didn't have a lot to say at half-time because they knew it. That first half performance was not what was required.
"In the second half we did pick it up and played some nice attacking stuff together, we scored two tries to their one. But we know if you give Saracens a lead then they are the masters of closing it out.
"They chip the ball in behind you and make you run from deep. We started to do that and conceded penalties. We gave them six kickable penalties and one that hit the post.
"You have to start well and get points on the board. We went with the wind for the first half and within three minutes we were 7-0 down. We have some work to do before we play Bath.
"We also gave away 19 penalties and free kicks today, that is just not acceptable," he added.
"We have got to look at it again because it now poses us problems in terms of selection. Our set piece was also under pressure, all-round it wasn't the day we wanted."
Hill admitted some of the attacking play from Warriors had been a positive, but conceded the team now needed to draw a line under recent cup performances.
"With the ball in hand we are scoring tries, both home and away," he said. "On a heavy pitch which is not easy to score on, we threatened and made line breaks.
"In terms of our attacking game, I feel that has progressed. But the other aspects of our performance, in terms of our discipline and tackling, will need to be addressed.
"We wanted these two games were going to be a stepping stone. Now we have to draw a line under them and mentally get ready to play Bath."
COACH READY TO CHANGE IT UP FOR BATH
Boss Richard Hill admitted he would need to consider his selection very carefully when the Aviva Premiership resumes with an away trip to Bath Rugby next Saturday afternoon.
Warriors will head to The Rec to face Bath - who are one point ahead of them in the league table - on the back of a disappointing 22-12 defeat to Saracens. Bath by comparison ran riot at Kingsholm to defeat Gloucester in the LV=Cup.
Hill admitted the home loss had left him with some selection issues and that the set piece and discipline would need to be improved in the West Country.
"That performance has caused me headaches," said Hill. "I would have liked to have seen a good performance against Saracens and then I could have penned in a few people.
"But clearly the way our set piece went is a big concern. With the front five we had we would have expected to dominate the scrum. There is also the discipline to look at.
"It has not made my life very easy because clearly if we go with that team next week, on that performance, we are going to get pumped. We will need to look at selection carefully.
"I'm not saying wholesale changes, but some will need to realise that that is not acceptable and that level of performance is not good enough.
"Clearly changes will have to be made," he added. "There are people who were not here today that can come into the side. Those that played well will know it; the others will know they can't expect to be selected next weekend.
"We all realise we need to produce something special to win next week. Bath have a good defensive record and can threaten you in attack. We have to look at defence and set piece.
"We can win there, but we will be underdogs and need to produce a special display.
"Bath have had a very good win today and that is no mean feat to go to Kingsholm and get a bug win against Gloucester.
"They are hitting some form and have a European quarter final to look forward to too. I'm sure they will look at us and think it is a game they should win.
"We have got an almighty week coming up to really pull ourselves around. We need to be positive and train hard before we have a hell of a game at Bath."