The striker scored twice as Nottingham Forest secured an impressive win at the City Ground, with Jair Cunha also finding the net. Rayan Cherki briefly gave City hope after the interval, but Delap's second goal restored Forest's two-goal advantage and settled the contest.
Delap felt the result reflected the work his team had been putting in, even when their performances had not been rewarded in front of goal.
"It's been coming and we've been performing like that every week and not putting it in the net. Today we showed we can put them in the net so we're all happy.
"We did everything right, we got the three points and we're going to be happy going into the international break."
The forward's first goal came after he made a determined run before getting his shot away, and he admitted there was little complication to his thinking in the moment.
"I just wanted to run and shoot, luckily I got there and it went in the net."
His second strike proved particularly important after Cherki had reduced the deficit for Manchester City. Delap was delighted to give Forest some breathing space again, and praised Morgan Gibbs-White for providing the assist.
"It gave us a little breathing room. It's always tough playing City, you're running after them for 90 minutes so we knew it was going to be a battle.
"It was a perfect ball from Morgan [Gibbs-White], he's set up a lot this season that we've not been able to convert so thankfully we could put it in the net."
The victory was a significant result for Forest, who had to withstand periods of pressure against a City side renowned for controlling possession. Delap's contribution ensured that their attacking work finally translated into a convincing scoreline.
For the striker, the most satisfying aspect was seeing the team turn their recent performances into a result. Forest now head into the international break with three points against one of the league's strongest sides and renewed confidence in their ability to convert chances.