Worcester coach Richard Hill said the sin-binning of "unlucky" Josh Matavesi was the turning point in their 24-18 defeat to Exeter.
The incident 10 minutes from time hurt the hosts, who had rallied from 14-6 down to lead 18-17.
However, Matavesi's yellow card for deliberate offside sealed their fate and Hill said after the 24-18 defeat: "Josh thought the ball was out and was unlucky to get the yellow card. With 15 men I think we might just have held on."
"But I am really delighted with the way we fought back and our driving maul paved the way for two tries.
"I must give credit to our forwards coach, Nigel Redman, who kicked a few backsides after last week's poor performance (at London Irish)."
The Warriors also seemed unlucky not to be awarded a first half try when David Lemi went over after a superb cross-kick from Andy Goode - but the try was ruled out by the touch judge for a knock-on by Lemi.
Hill added: "It looked a good try to me and everybody else in the ground. It knocked the stuffing out of us."
Exeter coach Rob Baxter was delighted with the result but worried about the way the Chiefs let Worcester back into the game.
"Any away wins in the Premiership are big wins. Worcester don't lose many at home but we controlled the first half as we played with a very high tempo," he said.
"However I was disappointed with the first 20 minutes after the interval as we became very edgy and tried to eke out a win when we should have continued to play as we did in the first half."
It therefore took a try two minutes from time from Dean Mumm to keep alive Exeter's hopes of European Cup rugby next season.
Baxter added: "We are one of the form teams in the Premiership with and three games to go we still have every chance of a return to the Heineken Cup."