Spurs lost Sunday's (AEST) showpiece final to Liverpool, losing 2-0 in Madrid.
The Spurs manager admitted his side's game plan was undone when Mohamed Salah scored a penalty for Liverpool after two minutes of play at Wanda Metropolitano.
Divock Origi's late strike put the game out of Tottenham's reach, but Pochettino had nothing but praise for his side's efforts.
"We can be proud of the effort, how we fought to arrive at this final," Pochettino said.
"We were very unlucky. We conceded a goal from a penalty but to the end we were alive, fighting, I think we played so well. It was a tough situation that changed completely our plans.
"It's not easy to play a team that plays transitions very well, taking risks. I feel so proud.
"Our fans have seen their team in the [UEFA] Champions League final for the first time. It's time to be optimistic about the future."
Pochettino reflected on Liverpool's achievement in bouncing back from having lost the 2018 final 3-1 to Real Madrid to clinch the trophy a year later and said his players had set themselves high standards.
Tottenham finished fourth in the Premier League, 26 points behind second-placed Liverpool, but Pochettino indicated that he felt another shot at the UEFA Champions League title was within their reach.
"We have to learn from this experience," the Argentinean said. "Liverpool did that last year and was in a different position today.
"I am so happy to manage this group of players but I congratulate Liverpool for a fantastic season.
"The standard [we have set] is so high. It wasn't enough today. When you live this experience you want to do it again. We hope to repeat it in the future.
"Always, it is about trying and believing. Hopefully it will happen again as soon as possible."