Wasps ended Bath's 15-month unbeaten home record in the Guinness Premiership with an extraordinary second-half performance at the Recreation Ground.
The visitors, needing a win of any sort to preserve their hopes of reaching the play-offs, ran in five tries to claim a bonus-point win.
Edwards admitted: "If we had lost today we would have been out of the play-offs."
And McGeechan added: "We've had a bit of catching up to do after the World Cup. We've got to perform as well as we did today every week.
"I'm really pleased. We were making some basic errors in the first half and we knew that if we were to do that then Bath would hurt us.
"But the 20 minutes after half-time was as well as we've played this season."
Commenting on former England full-back Josh Lewsey's two-try performance, McGeechan said: "Josh is really enjoying his rugby at the moment and it shows."
Bath head coach Steve Meehan reflected: "It was terribly frustrating - almost inconceivable.
"Defence has been one of our strengths over the last 12 months.
"Wasps played well but to loose a grip on our defensive systems was unacceptable, added Meehan - whose side were outscored five tries to four.
"Our indiscipline gave them their opportunities in the first half so we had to make sure that it didn't happen again.
"But in the first 20 minutes of the second half we just didn't get our organisation right. I'm not sure why."