Defender Danilo gave Pep Guardiola's side the lead with a fine 20-yard effort on 22 minutes.
“I'll start with the fans because I thought they were fantastic today," said Dyche.
“They know some of the challenges in front of us and that they've got a team that will give everything, even on this tough run.
“They (City) are the top side in the division, but the energy the supporters brought today was absolutely fantastic and that's something that's changed over a number of years here.
“Their confidence allows the players to play and on top of that, the players delivered."
Dyche, who changed to a 4-4-2 system, with Sam Vokes restored to partner Ashley Barnes, added: “We'd been beaten 3-0 and 3-0 by City in two games, so we had to change something.
“We wanted to play long and strong today and disrupt City, but the quality going into the front wasn't what we needed in the first half and we didn't put enough crosses in.
“We still had a really good chance, but in the second half, after weathering a very good start from them, you could sense us growing into the game.
“Their keeper makes an unbelievable save from Aaron and they went down the other end and missed an unbelievable chance and the energy went even higher in the crowd.
“It all changed in that couple of minutes. Suddenly the energy in the crowd grew. We started to find our feet and it's hard for them to constantly have the game in their favour over 90 minutes. We made sure they didn't and ended up scoring a fantastic goal."