A 4-1 defeat at Manchester City in the Premier League was hardly the result Blackburn wanted going into Thursday night's cup clash but Allardyce was in bullish mood ahead of the match.
He said: "You are always going to get rumours in the the Premier League. Never a day goes by without a positive or a negative story.
"You are bound to get some negative scenarios going around when you have not won in a while.
"You just get on with your job and that is what I will do. I have no great concerns at all."
O'Neill is backing Allardyce to haul Blackburn out of their mire.
A Villa victory on Thursday may push Allardyce closer to the brink if rumours of dressing-room unrest and unhappiness at boardroom level are to be believed.
But O'Neill is convinced 'Big Sam' can turn the tide, even if Villa go on to reach the final at Wembley.
He said: "I would absolutely back Blackburn Rovers.
"I didn't realise they had not won for so many games, but I wouldn't think, with Sam in charge, they will have any problems.
"I don't know anything about him being under pressure, but we're all only a couple of games away from a crisis.
"That has been proven, not just recently, but over the last number of years.
"It's a precarious enough job, but at the end of it all, we're all just two results away from potential disaster."
Rovers' last victory was the penalty shoot-out triumph over Chelsea in the quarter-final on December 2, but O'Neill feels the lean run will have no bearing on Thursday's outcome.
"Their efforts against Chelsea in the previous round were fantastic and I'm sure they'll draw on that sort of inspiration to get them up for this game," added O'Neill.
"I'm sure they'll be well up for it anyway. It's a semi final, two games away from Wembley, and that in itself is a massive incentive.
"Therefore I don't think previous recent form will have any bearing whatsoever on the game."
Aston Villa 11/8, Blackburn 2/1, Draw 9/4
Source: Team Talk
Source: Team Talk