The skipper headed home in the 61st minute to bring his side level at the Etihad Stadium as they threatened to halt the Premier League leaders’ long winning run.
But two goals in the final 10 minutes from Gabriel Jesus and a Riyad Mahrez strike eventually saw Pep Guardiola’s team claim a 21st straight victory in all competitions.
Coady’s goal was only his second in 224 league appearances for Wolves but he said: "It means nothing when you lose.
“It was nice at the time because it made it 1-1 but we needed to kick on a little bit. To score is great but it doesn't mean anything when you lose.”
City had taken the lead through Leander Dendoncker’s first-half own goal and Wolves, who did not have a touch of the ball in City’s penalty box before Coady’s goal, were thankful to goalkeeper Rui Patricio for making a string of stunning saves.
Coady said: “It was about staying in the game. We know what a good team they are. That was our way of going about it.
“You go 1-0 down and it's about staying in the game. We can't let the game get away from us like it did. We're gutted.
"No one is frightened about being on a football pitch. They're world class but we wanted to test ourselves. It was about staying in there and I thought we played some really good stuff. It's disappointing from our point of view."
Boss Nuno Espirito Santo admitted his team had paid for their mistakes after both City’s second and third goals came after Wolves lost possession in their own half.
Jesus completed the scoring with the final kick of the match with a goal given by VAR after initially being flagged offside.
Nuno said: “There are always positives and negatives. In the second half we were better with the way we pressed, the way we blocked.
“But the negative was we made mistakes which we shouldn’t have.
"Especially against City, when they recover the ball they press high and are very fast.
"But it's my responsibility, because we should grow in this aspect of the game. It's about us growing up and improving."
“The gameplan is always there but you are always facing another gameplan. It is difficult to plan against Manchester City when they have an advantage in the score and don’t allow you much possession.
“It is hard to create without the ball. In the second half we were able to have some good moments but weren’t able to sustain it.”