Mourinho tells his players to applaud the fans after the defeat at Anfield
The Londoners were beaten 4-1 on spot-kicks after Liverpool cancelled out Chelsea's 1-0 first-leg lead.
"It is a moment when everybody has to be strong," he said. "My players have a lot of reasons to be proud.
"We were the best team today, even against a team only playing for the Champions League."
"My players did a great run in the Champions League."
Mourinho also denied that his pre-match spat with Liverpool boss Rafael Benitez helped inspire Liverpool to victory.He added: "I respected Liverpool always in my words. I don't need to say more and today I think the best team was Chelsea."