Trailing the Portuguese side by a single goal as the game was unexpectedly hit by floodlight failure, the Reds were forced into replacing the injured Jonny Evans with Rio Ferdinand, then introduced Robin van Persie in place of Danny Welbeck.
An out-of-sorts display was forgotten after 80 minutes when the Dutchman levelled, before a Wayne Rooney penalty and Chicharito's close-range effort sealed an unlikely victory.
"It is a little bit surprising that we have scored three goals here tonight," Phelan told journalists at the post-match press conference. "In the first half we were not really doing anything in the game other than keeping possession of the ball.
"Possibly with the way the evening panned out – with the lights going out and the heavy rain, and then us having to make a quick substitution, bringing Rio Ferdinand on – I think that changed things for us, with the tempo of our game going up.
"Robin was instrumental in getting us further up the field. We played a little bit more in behind their midfield once Robin came on, and obviously he took his goal really well."
A fourth straight Group H victory guarantees United's progress to the knockout stage as group winners, underlining an immaculate response to last season's disappointing relegation to the Europa League.
"Our intention this year was to get into [the knockout phase] very quickly," Phelan said. "We were disappointing last year – the players and staff knew that, and I think the supporters wanted a reaction to that.