Having survived a scare when Raul Jimenez had a goal disallowed for offside, City hit the woodwork twice in the first half through Sergio Aguero and Raheem Sterling.
But Wolves then went ahead in hugely controversial fashion 12 minutes into the second half as Willy Boly turned in Joao Moutinho's cross at the far post with his right hand.
City were denied what looked a clear-cut penalty when David Silva was pushed over in the area before equalising through Aymeric Laporte's header. Aguero was thwarted by the frame of the goal again, hitting the bar with a 95th-minute free-kick.
Despite a frustrating afternoon in which his side suffered a first blip in defence of their Premier League title, Guardiola, who exchanged words with referee Martin Atkinson on the field after the game, was reticent to blame the officials.
"It's not my business, the Premier League will decide when the VAR will be here," Guardiola told Sky Sports.
On his on-field chat with Atkinson, Guardiola said: "I make a compliment for the job that's all."
Speaking in his post-match media conference, Guardiola added: "The game was what we expected. Wolves were organised, I'm not surprised but satisfied with how many times we created against them.
"Last season against 5-4-1 we had more problems to create chances. Today we had three posts and chances with the last pass or the last shot saved by the goalkeeper. But we also conceded chances.
"Normally we control counter-attacks quite well and we didn't but it's a good point for us because we knew the quality of the opponent and I think we created enough chances to win the game, but it doesn't count so at the end it is 1-1.
"I don't have too many regrets. There was a little lack of rhythm sometimes but in general I am satisfied with the performance."