But with Blackburn Rovers in control and Villa all at sea, Atkinson then failed to spot a push from Gabriel Agbonlahor on captain Ryan Nelsen, allowing former Rovers defender Stephen Warnock to fire the home side level on the half hour.
Manchester City snatch point at BlackburnFrom that moment the momentum shifted Villa's way, and when James Milner scored from the spot 10 minutes later, after Chris Samba was dismissed for a foul on Agbonlahor, the writing was on the wall for Blackburn.
After the break 10-man Rovers conceded three goals in nine minutes, sparked by an own goal from Steven Nzonzi, followed by a Milner strike that deflected off Agbonlahor and an Emile Heskey effort.
Blackburn at least restored some pride via a stunning overhead kick from Martin Olsson and a volley from Brett Emerton, only for Ashley Young to finish matters in injury time for a 6-4 win, 7-4 on aggregate.
Allardyce, though, was far from happy with Atkinson, heaping a significant portion of blame onto the official for the demise of his side's final dream.
"It's a bit difficult to take, scoring four goals and not getting through to the final," said Allardyce.
"We were in complete control of the game, and if anybody was going to score again it was us.
"But then the referee allows a blatant foul on Ryan Nelsen to go unpunished, and at this level you have to make sure the referee gets those decisions right.
"We are out of a cup final because of that decision perhaps. It is a major decision that has stopped us having the chance to go to Wembley.
"Whatever anybody might say, we were put in a position we should not have been put in.
"It lifted the crowd, it lifted Villa because they were playing very poorly, and then they are on their game.
"You could look at the fourth goal and say Agbonlahor had two arms on it and deflected it into the net for 4-2.
"Everybody thinks it's over, we're down to 10 men anyway, but then we managed to get back to 5-4.
"But the major part of us not getting through to the final is the referee, no question about it.
"Unfortunately, we have to suffer that. There's nothing we can do about it and we can't go to where we want to go, which is Wembley, and he is the major factor."
Allardyce did at least suggest his defence could have been tighter, only to draw himself back again to criticising Atkinson.
"There are obviously some areas where we can shoulder the blame for giving the goals away," said Allardyce.
"We've conceded six goals, and some of those we could have stopped, but the critical stage of the game is there for everybody to see.
"The big problem is that if a big decision goes against you at a critical time in the game, it makes a massive difference."
Ultimately, with the exception of Samba's red card, Allardyce had no complaints with his players, adding: "It was a gallant effort.
"They didn't feel sorry for themselves and kept going to the very end.
"I've nothing but praise for the way they've applied themselves in the end."