With three games left in the Aviva Premiership season, losing to Exeter means Worcester's chances of survival have slimmed.
Dean Ryan's outfit did pick up two bonus points against the Chiefs after scoring four tries and finishing within seven, but still trail Newcastle by seven points with the Falcons playing later on Sunday.
Worcester showed plenty of fight in coming back from 21-3 down to finish at 33-38 by the final whistle, but Ryan remains hopeful with three matches remaining.
"They were sharper and more clinical than us today. They caused us problems with their wide game stressing us a bit," said Ryan.
"But we are not going away yet. We have got a lot of things that we can contribute and we will see what happens after each game before we start being written off by anybody.
"We have three games to survive and we didn't win today. We didn't win because we were not clinical enough about understanding roles in the first half. Today was not good enough for half-an-hour.
"We have a couple of games to go. We know it is Bath and Saracens but funny things happen and if we can get it to the last weekend, we are back at home to make a very interesting closing day."