The Gunners' 2-1 win at the Bernabeu saw them reach the Champions League semifinals 5-1 on aggregate.
Arteta was beaming after defeating Real home and away: “I’m so happy, I think it's the third time in our history, so I have to be very proud to be there again.
"The team has shown incredible ambition, courage and willingness to compete against any opposition. It's not only the fact that we are there, I think it's the manner in which we've done it, both in London and here in Madrid, so I’m really proud of the players.
“It was my first time as a coach here, and today I realised how everything is possible in this stadium because they generate such chaos, such momentum. The crowd is really pushing them and anything can happen.
"But I think emotionally, especially after conceding, not scoring the goal with Bukayo (Saka), the way we handled that situation. These young players haven't been at this stage before, so it was remarkable.”
"We came here to win"
Going into the second-leg, Arteta insisted they would attack Real, rather than defend their 3-0 aggregate lead.
The Gunners manager continued: “The only thing that we discussed over the last three days was that we're coming here to win.
“It's not only about going through, it's in the manner that we have to do it in, because we are capable of doing it. Setting those demands and that mindset is very important for the team.
“ I think it shows the capacity of the team, that against any opponent, when we are at our best, we can perform. Especially with adversity and a lot of players that are not even involved here. The way we are doing it, I think it's special.
“Now we have to go to the semi-final against a team that we know very well, that we've already faced before. It's going to be a beautiful one.”