The Merseyside club were looking to secure a spot in the final which takes place on May 30, Steven Gerrard's birthday, as their talismanic captain hoped to call time on his Liverpool career in fitting fashion before moving to MLS outfit LA Galaxy.
And, although they were not playing particularly well, things looked to be going to plan when Philippe Coutinho broke the deadlock after half an hour at Wembley.
But Villa deservedly levelled through the in-form Christian Benteke shortly after and Fabian Delph scored what turned out to be the winner early in the second half.
The defeat provided another example of Liverpool surrendering on the big stage this season and Rodgers is starting to lose patience.
"Dealing with the occasion is something we need to improve at," he said in quotes reported by the BBC.
"There have been other big games where we have dealt with that very well, but there are others where we haven't.
"We need to focus on the performances and if we do that then normally we get the victories. But today it wasn't at the right level.
"Now we have to strive for top-four Premier League finish - it is an obligation of this wonderful club to fight until the finish."
Things could have turned out differently if Mario Balotelli had not seen an equaliser incorrectly disallowed for offside two minutes from time, a call that Rodgers was angered by.
He added: "It was a very poor decision. The official is looking across the line and should see the full-back playing Mario at least a yard onside. You need that to go for you."
