Arsenal produced a strong first-half display in Madrid and deservedly went ahead through a penalty from Viktor Gyokeres, who won and converted the spot-kick himself.
Atletico responded after the break when Julian Alvarez scored from the penalty spot to leave the tie finely balanced heading into next week's second leg at the Emirates Stadium.
Arteta praised his players for coping with the intensity inside the stadium and believes Arsenal are in a strong position ahead of the decisive clash in London.
"I'm very proud of the players," Arteta said. "I've seen some of the best teams in the world struggle here, but we handled the atmosphere and the occasion really well.
"We wanted to win the game, but the tie is still in our hands and now we have the opportunity to finish the job in front of our supporters."
The Arsenal manager was frustrated by the decision to overturn a penalty awarded for a foul on Emile Smith Rowe during the second half.
"What I am incredibly disappointed with is the way the penalty got overturned," Arteta said. "It was not a clear and obvious error and moments like that change games at this level."
Arteta also questioned the length of the VAR review, saying the incident was checked too many times before the referee changed his original call.
Despite the controversy, the Arsenal boss highlighted the performance of Gyokeres, who caused problems for Atletico throughout the first half.
"He was excellent in the first half," Arteta said. "He created the penalty, scored it calmly and gave us a big threat going forward."
Arsenal now return to London knowing a victory at the Emirates will send them into the Champions League final.
