John Terry took advantage of hestitation at a corner to put Chelsea ahead in first-half stoppage time before Diego Costa's shot deflected off Kyle Walker to settle the Wembley showpiece.
Mourinho called Tottenham a "fantastic team" following the game, praising Pochettino's work at White Hart Lane, and the Argentine says it was an honour to face off against the former Inter and Real Madrid boss.
"I admire Mourinho," he told reporters. "For me, he is the best or one of the best managers in the world.
"It was an honour to play against him, a dream for me. When I was a player I played against him and now to go face to face in a final at Wembley is a dream.
"I have full respect for him. I'm lucky that he thinks the same about me."
Tottenham enjoyed the best of the first half but struggled to break down a resilient backline marshalled by Terry, but Pochettino underlined his pride in his young squad.
He continued: "I think in the first half we were better than Chelsea and unlucky to concede in the way we conceded. In the second half we took some risks and they counter-attacked.
"I think we should feel proud of the players. I want to congratulate Chelsea. I'm disappointed for us and our supporters but I'm still proud.
"We have a very young squad - average age of 23 and a half years today - and for many players it was the first final. It's true that we will play a lot of finals in the next few years. I think we have a big future.
"It is painful. We are young, we need to improve but we are proud. We don't change our philosophy and believe in our style."
Despite losing the final, Pochettino believes the defeat can have a positive impact as Spurs continue their bid to secure a top-four finish.
He added: "Our challenge is the next game. We can't speak about the top four until the end of the season. We will try to get three points against Swansea.
"We need to forget about the final and move forward. We need to recover our legs and our minds because it's tough, but it's more positive than negative.
"It's important to play finals. It was a good experience for me but I need to improve. I think you can always improve. Now it's important to move forward and be strong for Wednesday."