Wanderers beat League One title hunters Plymouth 4-0 thanks to two early goals from Kyle Dempsey and Dion Charles and second-half efforts from Elias Kachunga and Gethin Jones.
Boss Evatt said: “I’m very proud that the players are performing like this on a big stage.
“It’s unbelievable, they certainly are capable and it’s a great credit to them to play with that freedom in a high-pressure game.
“We always want to start fast. The last couple of weeks I really felt like the group was reinvigorated.
“The last two or three weeks, training has gone back to where I expected it to be. The standard has improved, the energy has improved and I think today has shown exactly what we are capable of when we put it all together.
“It is difficult to play like this because we are not direct, we are not physical. Although we scored on two set pieces today, it’s not normally our natural strength, but what we are is a very exciting team to watch.
“Games are sometimes wide open, we give up on opportunities, we know that, but we back each other to take advantage of the opportunities we create and we did that today. Some of our play and bravery in possession was outstanding.
“We have suffered against some of the best teams, we have lost in the big moments, but today was the first time we smelled blood and seized the moments, seized the opportunities and then grew even more from that and gained confidence. .”
The Bolton manager admitted that the height of his victory at Wembley could challenge him to keep his players’ focus for the remaining eight games of their League One campaign.
Bolton sit fifth, level on points with Peterborough and Derby, as they aim for a play-off place.
Evatt said: “It’s going to be tough to bring players back to the ground and refocus, but we’re going to work tirelessly to make sure we do it.
“Days like today are addictive and we have the chance to come back here in May, but first we have to work very hard for the next eight league games to make sure we’re in the play-offs.”
Bolton picked up their first piece of silverware since 2004 and highlights the journey the club has been on since its revival after going into administration in 2019.
Evatt hugged chairman Sharon Brittan before the trophy was lifted and hailed the club’s turnaround under its ownership group.
“I said that she should be really proud of what she has achieved and the rest of the ownership group. They took over this club when it almost ceased to exist,” she said.
“They have rebuilt it from top to bottom.
“They have acted with such dignity, professionalism and honesty, not only in the football department but also in the community, the city, and when so much work goes into rebuilding a football club that was completely ruined, you deserve days like this.
“She certainly deserves days like this, just like the rest of the ownership group. They’ve been absolutely brilliant.”
Sub-par Plymouth rarely threatened in a one-sided game, with manager Steven Schumacher saying: “Obviously I am devastated with the result.
“I think congratulations are due to Bolton Wanderers. I think they were the better team and they deserved to win the game.
“We also want to apologize to our fans who didn’t want it to be like this.
“After the start of the game, we had: 10 minutes, 2-0 behind us, giving away the ball in two poor areas and they were punished.”