Rafael Benitez was left to rue missed opportunities as his Liverpool side failed to reach a third Champions League final in four years.
Fernando Torres and Ryan Babel goals were not enough to stop the Reds losing 3-2 at Chelsea, and the Liverpool boss said: "We did not finish our chances.
"We did not play as we can in the first half but in the second, and early in extra-time, we were the better side.
"But we could not capitalise and their goals killed us. I'm still proud."
Didier Drogba got two of the Chelsea goals in a man-of-the-match display, but Benitez - who had accused the Ivorian of diving - insisted he did not regret his pre-match comments.
"I don't think so," he said. "When you play a semi-final in the Champions League I don't think you think about anything other than that and that's the same for him (Drogba) I'm sure."
And the Liverpool boss dismissed suggestions his comments had inspired Drogba.
"More motivation than to play a final? No, I don't think so," he said.
Benitez added he had no complaints about the referee, who awarded Chelsea a penalty when Sami Hyypia brought down Michael Ballack but waved away appeals at the other end after the defender went down after a challenge by Drogba.
"The referee was OK, I cannot complain for the referee because I think he was not bad. Sometimes it is for you, sometimes against, but I think he wasn't the difference," said Benitez.
The Spaniard also explained his decision to withdraw star striker Torres straight after Chelsea's second goal, saying: "He had a problem with his hamstring.
"I was talking before with him, he told me he was not 100% so we needed to change him."
Benitez insisted he was "really" proud of his team, adding: "I think they worked really hard until the end. When we scored the goal we were in the game".
But when he was asked whether he felt his side deserved more over the two legs, the Liverpool boss said: "I think so, especially the first game. It would have been a big difference to come here with 1-0 rather than 1-1."
Liverpool led 1-0 deep into injury time in the first leg before John Arne Riise's own goal handed Chelsea a share of the spoils.
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