Campbell says that the Bluebirds did not underestimate the strength of their opponents.
"They had a centre-midfielder playing centre-back so you know you're going to get a bit of opportunity there," he told Sky Sports 1HD.
"But Man City have got a great squad of players and they're all internationals so we knew it was going to be difficult, but we knew we'd get chances.
"There was some great deliveries into the box today and it was a great all-round team performance.
"It was very special (scoring twice) but the most special thing was getting the three points today. When you're a promoted side you don't want to wait too long to get points on the board so today was a massive bonus for us.
"The manager's been saying to us that we deserve to be in this league on merit. We did very well last season in the Championship and we've got to go out there and show everyone what we're about.
"We're going to be underdogs for a lot of the games this season but as we showed today we've got the determination and hopefully that will see us through."
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