The England defender limped out of the action after just 18 minutes of the match but the damage is only superficial.
Guardiola revealed: "He had a huge kick in his knee. He could not run and that’s why we changed. Now when you see his knee it is swollen – but it is just a kick, not ligaments or anything."
Hull put up stubborn opposition and threatened at the start of the second half before City finally broke the hosts' resistance with goals from Yaya Toure, substitute Kelechi Iheanacho, plus a late own-goal from Curtis Davies.
After watching his side secure a third successive Premier League victory Guardiola declared: "It's not enough."
The Blues moved into second place and kept pace with leaders Chelsea, but are still seven points behind.
Guardiola said: "Except the first 10-15 minutes of the second half, we played good, in the first half we forgot the goal was there.
"In the second half, especially Sterling and our strikers, they saw a little bit more the goal and after the first goal it was easy."
Guardiola added: "It's important for us to get three victories in a row, it's not enough because the other teams are strong as well. Now we're going to rest and prepare for Anfield."
The boss revealed he gave his players a tactical talking to at the break and he was happier with what he saw thereafter.
"I spoke with the strikers, all of them," he said. "The winger has to be the wingers. You have to try to dribble and attack the goal. In the first half we didn’t do that; in the second half it was much, much better."
Finally, Guardiola had a word about his debut Boxing Day match, adding: "It's nice, I appreciate it's a special day - it's about the fans, it's a special day after Christmas day... it's a huge tradition and a marvellous tradition and I'm glad to be a part of it."