The Gunners won 1-0 thanks to Kai Havertz's injury-time strike, with Arsenal reaching the final 4-2 on aggregate.
On going to Wembley, Arteta said: "I can't wait because we've been working really hard over the last few years. We've been very close many times and we really want to enjoy that moment.
"(I'm) very happy, especially the way we ended up at the end with Kai's goal and the celebration of the players and staff, all together, because we knew how much it means.
"We really wanted to get to Wembley. I think overall, on the two legs, I think the team was extraordinary. I think we really deserved to be where we are and we play against a team that is very, very competitive and very difficult.
"With our people, I must say that the atmosphere they created was amazing tonight. We are where we want to be, so we're going to be in Wembley in a few weeks' time."
Asked about Havert's winner, Arteta continued: "That's the moment when you work so hard and a lot of people work so hard every single day. It's for those moments, to score that goal, all together, celebrating, a big smile and a lot of energy and pride. We fully deserve to be in Wembley in a few weeks' time, so let's enjoy it.
"That's the first trophy that we're going to have the opportunity to win. So, let's go for it."