Los Rojiblancos took a first-half lead through a headed goal from Joao Miranda, but Hulk equalised for Luciano Spalletti's side on the hour mark on Wednesday night.
Arda Turan put Atleti in front again, before Leo Baptistao secured the victory, scoring his first competitive goal for the club a minute after coming on as a substitute.
Despite Wednesday's victory, Simeone downplayed Atletico's chances, instead pointing to the Champions League experience of two of their group rivals.
He said: "For me, Zenit and Porto have been in the competition the longest and their players have more experience than ours, and from what I know of this tournament, that means Zenit and Porto are best placed to go through."
Despite his perspective on how the group might turn out, the Argentinian was pleased with how his players had performed over the 90 minutes.
"We dominated the pitch and space in the first half, we had a lot of chances and although we didn't take them, I had a feeling we would score eventually, which we did at the end of the first half.
"Zenit grew in the second half and attacked us from midfield and troubled us, and then the equaliser arrived."
But he added: "The team reacted very well (to the equaliser) and got back into the game. With the third goal we rounded off a very good performance."
The coach was also full of praise for Adrian Lopez, who made his first start of the season and received a standing ovation from the home crowd when he was substituted.
"Adrian is a very important player for us, he worked his guts off when the team needed him," Simeone said of the winger, who was included in the starting line-up due to the suspension to Diego Costa.
"He knew the best way to approach the game, even when he was given little space, and he also worked well defensively. We need him, the players love him and the fans know what he is capable of and I hope the support the fans gave him will help him grow in confidence."
Spalletti admitted that Hulk, who was substituted with five minutes to go, was not at his best as he was still recovering from a muscular injury.
"Of course when a player returns from a serious injury he plays with caution but he's on the right road to recovery and he played longer than we expected.
"Our plan was for him to just play 60-70 minutes because he's the type of player who can create a chance out of nothing," explained the Italian coach, who also conceded that Simeone's side were the stronger team on the night.
"Atletico were on top form tonight, they gave everything," he said.
"They have a good spirit and are growing at an alarming pace. They are a team of battlers, they are strong and in individual situations they outdid us."