The Italian was powerless to prevent Zenit going down to defeat in their Group G opener at the Vicente Calderon on Wednesday, as goals from Miranda, Arda Turan and Leo Baptistao gave the Spaniards the points.
Hulk briefly levelled in the second half with a magnificent strike from range, but ultimately it counted for little.
And Spalletti believes that the Liga side are a rising force on the continental stage.
He said: "It can be seen that Atletico are now in very good shape and going through a great moment.
"All the players are in good physical order and there are no such situations as we have, for example, with Hulk, who played his first match after injury.
"All (the Atletico players) are great. It is evident that the team are on the move.
"They have shown fighting spirit and in this match they have surpassed us."
Zenit forward Danny was also not surprised by the quality showcased by their Spanish hosts, but he was quick to stress that the Russians can bounce back.
He said: "Atletico is a great team. We have many matches left so we have to try and get good results."
‘The pure simplicity of the way Slot has managed the squad is probably the biggest thing I could say about him. It’s not broken, so let’s get on with it’: Liverpool legend full of admiration for Jurgen Klopp's successor at Anfield
‘I trained at Spurs and thought they’d give me a chance. But I received a letter thanking me but saying they didn’t think I was good enough – I was gutted’: How Tottenham missed out on signing Wales legend John Toshack
