Quins outscored their opponents three tries to two but the kicking of Dave Walder - in for England outcast Danny Cipriani - denied the visitors a fourth straight victory.
"That team does not have many caps between them, but they are getting better and better and are disappointed we didn't win," said Richards.
"Not many sides come to Wasps and have the opportunities to win, but we did. There's a good spirit in the camp and you just keep working.
"The spell either side of half-time hurt us. They slowed the ball down and we were not getting any assistance from the referee. We tightened things up and that made a huge difference.
"We wanted a win and I have no qualms about the decision-making at the end. We had three tries and whatever you do it's one of those things. Sometimes it comes off and sometimes it doesn't."
Bristol coach Richard Hill was relieved to finally end his side's dismal record on the road after they came from behind to beat rock-bottom Leeds 30-13.
Scrum-half Shaun Perry, who helped himself to two of the visitors' four tries, was singled out for special praise by his boss.
Hill said: "For him to come back after a nasty throat injury - it was a bizarre fracture of the windpipe - and play like that showed what he can do.
"He bullocked his way over for two tries and I was very pleased with the second-half performance from the boys."
Leeds chief executive Gary Hetherington insists relegation will not deter the club from building a bigger and better squad.
He said: "Irrespective of whichever division we are in next season, it will not alter the plans and the strategy at all.
"That is to retain our better quality players and add at least six new players.
"I'll be travelling to Sydney very much on a player-recruitment mission."
Sale director of rugby Philippe Saint-Andre tried to take the positives from his side's 24-20 defeat at Saracens.
The visitors came back from 21-0 down to snatch a bonus point from the game.
"We did good things but we gave them two tries," Saint-Andre said.
"That makes it difficult but we showed a lot of character.
"We came back with one bonus point - it's better than nothing. We have a big game on Friday at home to Gloucester, and we need to win."
Full-back Mark Cueto could be struggling to play on Friday.
Saint-Andre revealed that the former England player had damaged a hamstring and confirmed he was to undergo a scan on Monday morning.