City took the three points thanks to first-half goals from Darius Vassell and Benjani Mwaruwari and in doing so completed their first double over United since the 1969/70 season.
The match marked the 50th anniversary of the Munich air disaster and Hamann told Sky Sports: "We worked ever so hard today and didn't give them much space when they went forward. Every time one of our players lost the ball another player covered and won it back.
"We know how good they are going forward and to restrict them to one goal and a handful of chances throughout the 90 minutes showed how well we defended today.
Hamann praised the performance of striker Benjani, who marked his first start for City by heading in their second goal.
"He's done ever so well," said Hamann. "He kept the ball well and worked hard. When we put the ball in the channels he was always chasing it and won a few free-kicks.
"He scored a great goal and it was a great debut for him."