The Latics were behind at half-time and deservedly so, but in a complete turnaround in momentum claimed a vital three points thanks to goals by Dean Furman and James Tarkowski.
The result ensured they leapfrogged Colchester in the table but it is now eight defeats in 10 games for Stevenage.
Philliskirk said: "We were a little bit lacklustre first half - we were second best and the lads looked a little tired.
"Fortunately, we started the second half very well, but the players have got a bit of ownership at the moment and I challenged them to put into practice what they were saying.
"Actions speak louder than words and I was saying 'it's alright saying it lads, get your fingers out and do something about it'.
"And fair play to them, I thought in the second half we controlled the game for half an hour and went 2-1 up."
Stevenage boss Gary Smith was fuming with his side's second-half showing, saying: "On the behalf of everyone in that changing room I have to apologise to the fans for the display and the result.
"It is the most disappointed and dejected that I've felt since I've been here and it came out of the blue.
"I thought the first half was probably everything we could have wanted other than to extend our lead because we had opportunities to do that. The second half was everything that we really don't want to be about, which was second best and eventually point-less."