Sergio Aguero struck twice to take his career goal tally to 400, while Raheem Sterling was also on target with his fifth goal in the opening three Premier League games.
Their second victory this season ensured second-placed City remained two points behind leaders Liverpool.
Speaking in a post match press conference, Guardiola acknowledged his side had been forced to work hard for the win.
He highlighted the ruthlessness of City’s finishing as the decisive factor on a hot day at Dean Court.
“It was a tough game, we knew it would be. We have seven points. We should have nine, but it’s OK.
“It’s a nice three points but we have a few things to improve. They were stronger than us in the boxes. But the quality of our players in front made the difference,” he said.
