Jacob Murphy and Anthony Gordon struck for the 2-0 win, with Newcastle reaching the final 4-0 on aggregate.
Howe said afterwards: "I'm really pleased. We had a really long wait between the ties, a long time to think about our lead and had a lot of discussions but I am just delighted with the way we played. I'm delighted with how we handled the occasion and managed the performance, so pleased to be through to the final.
"We wanted to be ourselves. Attack, press high, everything we always want to do, we tried to do and implement it. Arsenal are a very hard team to press, there's a lot of movement and rotations of players, but the players executed it excellently. I was really pleased with that aspect of our game today.
"I thought we counter attacked very well today too. There was a lot of energy in the side, it was much better than the weekend against Fulham. A great win.
"We have come a long way since then (the 2023 final v Manchester United) - the Champions League does that to you, it is so testing and unique. Naturally for the big games a lot of the players have been there before, and we are used to the quick turnarounds and work smarter.
"There is a good feeling about the squad. We are tight on numbers but big on energy. I would love to think we can go to Wembley and perform better than we did previously."