Edwards, a possible England target following their disappointing World Cup, is moving on after 10 years at the club and he received a standing post-match ovation from the 8,222 crowd.
He said: "The game of rugby is about the players, not the coaches, and I've had some magnificent players to coach during my 10 years here."
The highlight of his decade was, he said, the 2004 and 2007 Heineken Cup triumphs.
"For a club relatively small in stature to beat the big French and Irish teams and win the Heineken Cup twice was a tremendous effort," added Edwards.
Prop forwards Soane Tonga'uiha and Brian Mujati scored the tries which powered Northampton to their fifth successive victory.
Fly-half Ryan Lamb kicked the other 14 points for Saints who, strengthened by the return of their international contingent from World Cup duty, have put a poor start to the season firmly behind them.
Wasps, denied their third successive Premiership win, replied with tries by England centre Riki Flutey and lock Ross Filipo and a penalty from fly-half Nick Robinson.
But defeat provided a miserable end to a week which saw Edwards and veteran England lock Simon Shaw sever their connections with the club.
Wasps felt there was an unspotted forward pass in the build-up to Northampton's opening try from Tongan prop Tonga'uiha but director of rugby Dai Young refused to blame referee Tim Wigglesworth for the defeat.
He said: "Take it back two or three steps before that and we got turned over twice which gave them that opportunity to be there.
"I'm a big believer that you can only control what you can control and we have got to look at ourselves.
"It's no good looking for excuses elsewhere. You have to find a way to win and we didn't do that.
"The biggest grievance to us was the tackle area - how that was refereed or not refereed.
"Refereeing's not an easy job, otherwise everybody would be doing it. It's not fair to stand here and criticise. There's proper channels to do it and we're going to have to look at it if we feel there were mistakes made.
"On occasions we didn't help ourselves but I thought we were unlucky with a few calls. We got killed in the tackle area and it didn't help."
Young added: "First half we were the better team but we didn't build any score. Second half, Northampton had a really big first 20 minutes which got them in front."
Northampton rugby director Jim Mallinder believes his side will have to perform better when they open their Heineken Cup campaign in Ireland on Saturday.
He said: "We weren't brilliant today. We did enough to win but we'll probably need to do a little bit more if we're going to beat Munster next weekend.
"We conceded a sloppy try but generally our defence was quite good. But defensively, we gave away a few too many penalties.
"You've got to listen to the referee - and Mr Wigglesworth does things slightly differently - so you've got to work with him."
Saints have staged a revival, winning five successive matches in the Premiership and LV= Cup, since their World Cup stars returned and Mallinder said: "We've now got on a bit of a roll and we're keen on keeping that momentum going."
He added: "It's good to have threats all over the field, particularly when your props score in open play.
"To see Tonga'uiha finishing off a wide move and then to see Mujati running over backs is a pretty nice sight."
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