Redpath's men led by eight points at two separate stages in the match but ill-discipline and a couple of lapses of concentration cost them dear as Sarries scored a late try to triumph at Kingsholm.
"There were three or four dull penalties in the last 20 minutes, plus a mark that we probably could have taken that would have sealed that victory," said Redpath.
"You can't give away cheap penalties in your half and we did. If you do that, you'll concede points and you'll lose the game, and that's what happened.
"We have to be disciplined across the board, one to 15. You've got to be really smart at what you do: referees are picking up on the little things that you can't get away with. You have to accept that, get on with it and not look for excuses.
"We should never have been in that position at 17-9. We should have sealed the game off. That's what we need to be focussing on. The fact that we lost our home record is irrelevant."
Despite the disappointment of a first domestic defeat on home soil for 23 matches, Redpath saw plenty of positives in his side's performance.
Gloucester were the better team for large parts of Saturday's encounter, with their defence particularly impressive against a Saracens outfit who have now won six league games on the spin.
"I think we were in control for most of the game," added Redpath, whose team also face Connacht and Harlequins in Pool 6.
"We've been criticised for our defence but I thought our D was outstanding for the majority of the game. I don't think there were many chances where they could have scored a try.
"We missed a penalty and a conversion and I think we could easily have been five points further ahead at half time. But we weren't and that's what tight games are all about: you have to take your chances.
"We lost by two points to the team that everyone says is the best in the Premiership so I'm not too downhearted. I've been honest with the players and said the same to them but we tried our best not to win it in some parts."