Leicester were holding Arsenal at 2-2 before the hosts struck twice in injury-time through an own goal and Kai Havertz strike.
Arteta said: "I'm very happy, first of all with the performance. I think we were unbelievable today. We deserved to win with many more goals.
"Starting the second half the way we did, conceding the first goal makes things harder and then with the equaliser the team showed unbelievable character to keep pushing, creating chance after chance. We suffered more than we should have but this is football. Really happy with the team.
"Great. How we handled the situation, we felt it should have been many more and it wasn't and suddenly it is 2-2 but we had to deal with a very good team with difficult circumstances and we stayed really composed. We had a lot of clarity, understanding what we had to do and we kept doing what we had to do and we earned the right to win it. James Justin scored an unbelievable, world class goal."
On scoring two goals in stoppage time, he said: "Now we are really happy but we could have been in a very different position because of the two goals we conceded but certainty with the performance we have to be super happy."
On the chances of the match ending in a draw: "There's always a possibility, this is the Premier League, every team has got unbelievable resources to create issues and today they scored two goals out of very little but this is the quality that they have."