Tijjani Reijnders had City ahead before Omari Hutchinson struck an equaliser for Forest. However, Rayan Cherki then found a late winner for the visitors.
Guardiola joked afterwards: "All the kilos I won over Christmas time in weight, today I lost it. I am fit again. What a team Sean Dyche has made again. That's a really, really, really big three points.
"(Forest) are an incredible team, the way that they play they do it unbelievably. Igor wins all of the balls. They have a top quality team, This team was in the Champions League but for one or two games last season and now in European competitions. A fantastic team and tough place to come, and at winter time.
"We talked a lot about this in the last few days with the players. Winter time, at Nottingham Forest, you have to be there, there, there. Today if we are not ready then we do not win that game. The mentality was unbelievable, so really pleased again for the guys."
On changes from first half to second, he continued: "There were too many players behind the ball and not the pockets. After when we break, move inside and outside, then we create chances.
On celebrating with Pep Lijnders after both goals, Guardiola said: "He is so good. He is a top manager. Sometimes people think, 'he's the assistant', well maybe I am his assistant. We talked at half time and changed a little bit the shape.
"We have 18 games played so we have now finished the first leg. And in the second we know that coming is a lot of games like today. The Premier League is tougher, tougher, tougher, but it is important to be there. Winning or losing today would not mean it's over, we have many games."