Thomas Partey put Atletico ahead in the first leg of the last-32 tie at Elche, but the hosts levelled through a second-half Lolo Pla penalty.
Gonzalez, 22, and Moya, 19, made their Atletico debuts as Simeone's side were held by third-tier opposition.
Simeone praised the pair for their displays, particularly given the situation.
"Sergi played very well and Toni Moya played calmly, even though the match was anything but calm because of the result," the Argentinian told a news conference.
"He played with personality and we like that."
The result left Atletico with work to do ahead of the second leg at home on November 29.
Simeone said: "We worked very hard in the first half and we had lots of chances.
"In the second half, Elche started off well and earned a penalty.
"After that moment, we had chances to settle the knockout round, but we'll have to do so in the return leg."