Blues would have secured an immediate return to the top flight with victory but defeat leaves them one point clear of Sheffield United ahead of a tough trip to Reading on the final day, while the Blades face Neil Warnock's Crystal Palace at Selhurst Park.
Preston, meanwhile, are up to seventh in the Championship, two points behind Burnley who occupy the final play-off berth.
McLeish, who claimed dramatic final-day titles with Rangers during his stint in charge at Ibrox, said: "I am bitterly disappointed but we have to bounce back straight away.
"We know that we blew this opportunity today and we have one left to get up to the Premier League automatically.
"They were two brilliant goals and sometimes you can start splitting hairs to analyse why you lost.
"We had our opportunities, we had some of the game at 1-1, but it didn't go for us.
"We have to go and win at Reading and I'll make sure that every player is aware of my feelings on that and the positive side of things in the coming week.
"Of course the players will be down but can we still win it at Reading? Of course we can."
After Sean St Ledger had somehow missed a point-blank header within minutes of the restart, Keith Fahey sent the crowd into raptures when he headed home at the other end just before the hour.
Lee Bowyer and Lee Williamson were both given their marching orders shortly after for wrestling each other in the centre circle, a decision both McLeish and opposite number Alan Irvine felt was harsh.
Paul McKenna then silenced a buoyant home crowd when he celebrated breaking Sir Tom Finney's appearance record for Preston by rifling home a superb 30-yard strike in the 68th minute.
Cameron Jerome put a clear opening over the bar from close range as the encounter went from end to end.
But Ross Wallace stunned the home fans when his 89th-minute free-kick clipped the inside of a post before nestling in the far corner, with the winger picking up a second yellow card for removing his shirt in celebration.
Irvine joked: "We've been working all season on goals like that but it's not come off.
"Great strikes, stunning strikes without any question. I hadn't given up because we'd come back from a goal down on many, many occasions this season.
"Even though this is as hard a place to come back as you can possibly find in the Championship, I still felt there were chances for us."
Ahead of the club's final game of the season at home to QPR, Irvine added: "If these results manage to get us in the play-offs then fantastic, it will be a great season for us considering where we were this time last year.
"If they don't then it's still great progress but obviously I want us to be in there when it really matters."