Having gone a goal down in the first half, Blackburn looked spirited in the second period but were unable to find the elusive equaliser, Nikola Kalinic being particularly unlucky to see two efforts come back off the woodwork.
As well as putting Villa firmly in the driving seat for next week's return leg, the result also means Rovers have gone nine games in all competitions without a win and Allardyce knows his players must quickly get their minds back on the job of picking up points in the Premier League.
"They were relatively down on the fact they thought they had done enough to at least get a draw (from the Villa match)," Allardyce said.
"They were disappointed and that's something we can't dwell on any more because the games are coming thick and fast.
"We can ponder over that game for a short time and have a little look at what was good and what was not so good, but really we need to put that to one side and focus totally on Fulham.
"I've got to try and make sure there's no lingering doubts about how important the game is and how important the three points is."
With the second leg of the semi-final coming just three days after Sunday's match, Allardyce is also wary of his players letting their thoughts drift too far ahead.
"They cannot just be looking after themselves for Wednesday's match at Villa Park," Allardyce said.
"That's one of the big tests for me and the staff here, to make sure the lads give their very best on Sunday to get that three points - and that will help us if we are to overcome the big task against Villa."
Blackburn have not tasted victory since their quarter-final triumph over Chelsea at the start of December and Allardyce admitted everyone at the club was desperate to rediscover that winning feeling.
He said: "We're all desperate for one now. We're all worrying where the next win is coming from and it has got to start very quickly because it has been a long time since we experienced the joy of winning.
"We want to get that feeling back again, feel what that feeling is like and hang on to it for as long as we can."
Source: Team Talk
Source: Team Talk