Late goals from Nico O'Reilly and Mateo Kovacic struck for the 2-0 win.
“I would say big. We had to be so smart,” Guardiola declared. “With five or six games left, winning here at Goodison Park in the moment that they have, winning at Nottingham Forest away and Arsenal could not win here.
“It’s massively important.
“What these players have done for a decade I am so grateful whatever happens and this season more than ever.
“We have had a tough period especially with injuries but now we are more or less stable."
The win takes City into fourth place, with Nottingham Forest fifth having played a game less.
Guardiola continued: “We are miles away from Liverpool but tonight we will see in a few hours what happens between Newcastle and Villa then Chelsea and Nottingham Forest. We will see.
“Now it’s in our hands.
“A final on Tuesday (at home to Aston Villa) then two more games home and away. Hopefully we can achieve the success of qualifying for the Champions League.”