The Hammers' Spanish shot-stopper could only watch on in horror at Upton Park on Saturday as he was beaten by a looping volley from close to halfway.
With Manchester United striker Rooney having spotted him off his line, Adrian lost his bearings while back-peddling and tumbled to the turf as the ball hit the back of the net.
That effort set the visiting Red Devils on their way to a 2-0 success and left West Ham just six points above the relegation zone.
Allardyce, though, will not be pointing the finger of blame at his shot-stopper, with Adrian having impressed on the whole during his debut season in England.
He said in the Daily Mirror: "I don't think he was at fault for the goal at all - it's a one in a million, a perfect strike.
"I said, 'Don't blame yourself for it, son. Get on with it. Don't let that affect you'.
"When you let one go right through your hands from eight or nine yards out and it's more like a back-pass than a shot, that would be more of a concern than a wonderful strike from Wayne Rooney.
"He's been outstanding for us. Over a season, good keepers earn you anything between nine and 12 points. He has been consistently good."
Defeat in their last outing has West Ham stuck on 31 points, and Allardyce admits they have work to do in order to preserve their Premier League status - starting against Hull City on Wednesday.
He added: "This is such a big game. It is a big six-pointer followed by another big game at Sunderland.
"We are either going to be very, very nervous by next Tuesday or we will feel a little bit safer."