The victory sees Leicester Tigers through to the quarter-final stages of Europe's top-tier for a second successive season and sets up a meeting with winner of Leinster and Ulster in their Round of 16 game on Saturday afternoon in Dublin.
When asked about his review of the side's performance, Wigglesworth said: "They didn't deviate from the plan when they [Edinburgh] got little bits of ascendency and put us under pressure."
"The lads kept calm, trusted in one another and fought out a committed performance.
"It's nothing I wouldn't expect from this group, fighting and scrapping for everything, but also how we were smart with the ball."
Wigglesworth left Jasper Wiese out of his starting side for the clash with Edinburgh and, after an injury in the first half to Olly Cracknell, was forced into bringing the back-rower on earlier than planned.
Wiese's 40 minutes included 8 carries, 10 tackles, 1 linebreak and a turnover, as well as a memorable finish for the fixture's lone try, which earned the South African the Heineken Star of the Match award at full-time.
Speaking about his No.8's performance, Wigglesworth said: "We brought Jasper on earlier than planned as Olly [Cracknell] got a bit of a knock in the first half and so brought Jasper in before we thought we would need to."
"He is certainly an x-factor, we all know that and have seen it from him before ... except for the twinkle toes finish, that's something new from him for sure.
"Ultimately, what Jasper and all of the replacements did tonight was come on the field and added to what the starting side had done. We always ask for a 23-man effort from the players and tonight we saw a performance and effort from every single player that was just that."
The match was played in predominantly rainy conditions, after a day of downpours, which the Leicester Tigers Head Coach said saw him ask his side to step up even more than usual in the set piece and territory battle with an Edinburgh side filled with Scotland internationals.
"You need to find an advantage in your set piece, you need to find an advantage with your kicking game and then back that up with effort, fight and those things," he said.
"Conditions aren't something you can control, but how you adapt to them and manage your game plan is what you can control.
"The lads managed it tonight, they stuck to what we asked of them and got the result which is most pleasing.
"I will take that committed, dedicated performance every single day of the week over anything else, I am incredibly proud of them tonight and hope the supporters are as well."
Cracknell and Guy Porter were both injury replacements in the win and Wigglesworth admitted it added to a growing injury list which includes Matt Scott, Ben Youngs and Chris Ashton, who were all unable to be selected after suffering "knocks" in recent weeks.
"We're down to bare bones in a lot of positions now, which isn't ideal, but we have been through it before and come out the other side," Wigglesworth said.
"This side doesn't make excuses, they don't whinge and don't complain, they just go out and work hard during the week to prepare properly for the next job ahead of us on the weekend.
"They deserve to enjoy this tonight and we'll keep an eye on tomorrow's game, see who we are up against, and then get to work to prepare as best we can for whoever is the next opponent."