Goals from Josko Gvardiol and Erling Haaland earned a vital win to move us with a point of title leaders Arsenal having played a game fewer.
Fighting for survival, Forest never gave up and created big chances at the other end, hitting the crossbar and having another effort cleared off the line by Gvardiol.
The City boss said the home side were more of a threat than when they picked up a surprise 1-1 draw last season.
“[It was] really hard,” he said. “Last season we drew and played much better than today.
“Knowing the circumstances that we arrived here, we knew the game that was going to happen.
“We were so lucky that the pitch was so dry. With the chances they had, with better pitch conditions, they would have scored.
“We were incredibly fortunate for that. We suffered but when [Mateo Kovacic] came on in the second half and Bernardo [Silva] was involved in there, we were much, much better.”
Sunday’s results guarantee our involvement in next season’s Champions League for what will be a 14th successive season.
And Guardiola said it is always a huge achievement and one that other Clubs would be delighted at.
“My CEO and owner will be so happy,” he said. “We are going to be in Champions League, how many teams would love that?
“It is really good news. I’ve said it many times that it’s the most important target. We did it with four games left. Big congratulations to the club and my players to achieve that.”
Arsenal secured their own three points shortly before kick-off with a 3-2 victory in the North London derby.
Spurs chased a late equaliser, but Guardiola says he expects the Gunners to win every game between now and the end of the season, meaning we will have to do the same.
“We prefer they lose but we cannot control what they do,” he added.
“They made a good result. There are four games left. I think they are not going to lose any points.
“We know what exactly we have to do.”