Wolves won 2-1, with Rayan Ait-Nouri and Rodrigo Gomes scoring for the visitors, before Scott Twine struck for City.
Manning afterwards insisted: "Tough game, conceding the goals early on made it a challenge. We were a little bit off. The intent was there but naturally if you play good players and you arrive a little bit late, you get opened up.
"I thought in the second half we controlled a lot without making many chances. We need to take the lesson from today and bounce into the league against Coventry.
"It's a constant process, you have to get better and keep turning up. Today was a big lesson, we probably showed them too much respect early on.
"You want to turn up and give the best account of yourselves. We didn't do that for 95 minutes."
On Bristol City hitting the bar late on, he added: "No idea how it doesn't go in to be honest. But yeah, shoulda, woulda, coulda.
"We're under no illusion we have a lot of work to do. But when you look at it, it wasn't a huge gulf in the second half, and that was the most pleasing thing."