A Branislav Ivanovic header at the start of extra-time gave Chelsea a 1-0 win on the night, and 2-1 on aggregate, to send the Blues into the final of the tournament and give them their first chance of silverware this season.
However, it wasn’t easy going for Chelsea in either game and Liverpool proved a stern test for the Premier League leaders, with goalkeeper Thibaut Courtois making a number of top saves to deny Rodgers’ side.
That has led to Mourinho going out of his way to praise his former protégé and the manner in which he has turned around their season following a poor start to the campaign.
"I think in the second half we were better than them and also in extra-time but I want to be honest, fair with them," he said after the game on Sky Sports.
"The way they started the season they were not going in the right direction. But he [Rodgers] was intelligent enough to change, to create a new team, because this is a new Liverpool and they were a very difficult opponent and I'm even happier because we beat a very good team over two legs."
Tempers were running high during the clash at Stamford Bridge, threating to boil over on more than one occasion during the affair, with Diego Costa avoiding a red card despite appearing to stamp on Emre Can before being denied a penalty later on in the game.
However, Mourinho refused to speak about the penalty claim under concerns that the FA will try to punish him for being too outspoken once again.
“If I speak, people will say it's Mourinho again,” he added.
“If I speak the FA will try to punish me as they always do so I think it is better for you to do it, but it's so clear, so clear, and that is difficult to accept, even winning the game, so I have to ask myself why.”