Philippe Coutinho put the Reds ahead, but they endured Wembley heartache after Christian Benteke and Fabian Delph ensured a 2-1 win for Tim Sherwood's men.
Rodgers holds an unwanted record of having failed to win a trophy in his three seasons in charge of the Anfield.
And he believes his players failed to rise to the occasion.
Dealing with the occasion is something we need to improve at
Brendan Rodgers
"Dealing with the occasion is something we need to improve at," Rodgers told BT Sport.
"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 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."