A late solo try from Jonny May kept Gloucester's hopes for the competition alive, while cup newcomers Connacht were extremely unfortunate to come away with a defeat.
The Irish province led for most of the game against an out of sorts Gloucester and were less than four minutes away from a shock win.
Niall O'Connor looked to have earned Connacht their first win of the competition when his 72nd-minute penalty put the visitors 19-16 up, but replacement centre May then sailed past two defenders for the decisive score.
Tiernan O'Halloran and Tim Taylor had earlier traded first-half tries while O'Connor kicked four penalties and Taylor and Freddie Burns combined for three for the hosts.
Redpath said: "It was a poor performance, we looked a bit nervous and a bit cautious. It was a great individual effort from Jonny May but I am relieved to win."
The Gloucester performance was so bad in the first half that sections of the crowd booed as the whistle blew for the interval.
Redpath said: "I accept that they were entitled to express their criticism. With the interception try (O'Halloran's), we gave them a dream start but we showed more composure after the interval."
A disappointed Connacht coach Eric Elwood admitted his side were downbeat at the late reverse.
"The dressing room is very quiet, we played extremely well and to lose in the way we did is difficult to take," he said.
"We've got to keep bouncing back and though it's tough going it hasn't broken our spirit."
The Irish forwards had shown huge commitment knocking Gloucester out of their stride and deserved to take the spoils.
Elwood paid tribute to their efforts: "We didn't play our best last week, especially up front but today they fronted up magnificently and give us a platform from which we could play."
With four defeats from four games Connacht now have no chance of progressing and Gloucester's hopes are also slim.
Redpath said: "Realistically, losing the first two games has made it difficult to reinstate our chances. We must concentrate on our Boxing Day game against Wasps as that it is a massive one and we need to go away and reflect and solve some of the issues for ourselves."
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