The Spanish club picked up three points on Wednesday as goals from Miranda, Arda Turan and Leo Baptistao were enough to see them open their Group G campaign with a 3-1 win.
Hulk briefly levelled the scores at 1-1 in the second period, but Simeone's men had too much.
But despite the win, Simeone is convinced that the more experienced duo of Zenit and Porto remain favourites to progress past the group stages, although he feels that Atletico’s squad depth gives them a good chance.
He said: "I repeat, Zenit and Porto are favourites.They've participated more in the Champions League. Our strength is to play well.
"The presence of Hulk and Danny was dangerous. When (coach, Luciano) Spalletti changed (at half-time) Zenit attacked well but defensively they retreated less."
Striker Baptistao's goal with 10 minutes left on his Champions League debut effectively ended the game as a contest, and he praised Atletico’s character after overcoming a "tough" side.
He said: "The team was very good. We played the game how Simeone wanted.
"We knew that the match was going to be very, very tough. Zenit have great players and we expected nothing less of them.
"Playing the Champions League is different. It was my first time playing in the competition.
"Hearing the anthem at the start was exciting."
