A quick-fire brace from wing Josh Drauniniu and late score from replacement flanker Jake Abbott saw Worcester mount a second half fight-back.
However, it ultimately proved in vain as Worcester ended the league season without a win on the road.
"Everything has been geared up for a big start - but our start wasn't good enough," conceded Redman. "The difference in the game was they used the wind early on, put us under pressure and scored two tries in eight minutes.
"Accuracy is something we have needed to be better at all season. Every now and then we do something that has proven costly. It's those little things that are the difference between winning and losing.
"We have come up short late on in games and had we been more accurate, with our decision making and execution, throughout the season it would have been a different story.
"I always felt we could win the game because what we needed was momentum," he added.
"The two tries from Josh (Drauniniu) started to do that before another error allowed London Welsh to gain territory and they got a penalty to kick their points.
"We knew London Welsh had nothing to lose, we knew they would throw the ball around. We wanted to adopt a more pragmatic approach and build of territory and take the sting out of them.
"But when you concede two tries straight away it hits that. There was still a lot of time and at times I felt we played very well.
"There were some good performances and Richard de Carpentier was outstanding, he showed some real glimpses of talent that he will build on for the future. These young players will play well in the Aviva Premiership and need the opportunity."
Redman also refused to blame recent off-field events as a distraction as Warriors ended the season with defeat.
He added: "The players have responded in a really professional manner to everything going on around them. They have had the right attitude and want to do well for Worcester.
"There are members of the team who are moving on, and we wish them good luck, but everything was set up to come to the Kassam and get our first away win and showcase our talents for a new Director of Rugby coming in.
"We talked about what motivates us and the preparation went well. I don't feel we ever chased the game and I still felt in the second half, when we gained momentum and came back into it, that we could win it.
"Inaccuracy has cost us. There wasn't enough consistency throughout our game and when you add it up you are never going win playing like that."