The north London side overcame Chelsea 2-1 in a dominant display at Wembley on Saturday.
With the season considered a disappointment after missing out on a top-four finish, the Spaniard was happy to finish the campaign on a high.
"It feels really good - we knew we had to win this game," Bellerin told Arsenal Player.
"We gave everything in every single moment of the game. I'm really proud of the boys for the work we've done throughout the whole year. It's beautiful to go on our break with another FA Cup.
"We knew their game, we knew they were going to go on the counter-attack but we were really confident in our new system. We knew we could play the ball.
"The team got in between the lines really well. We kept the ball really well and we even should have scored more goals than we did because we hit the post a few times.
"At some points I was a bit worried that could have cost us the game but it was a good reaction to 1-1 from Oli and Rambo. It's a beautiful feeling."