Sarri's side have lost their past three away Premier League games by an aggregate 12-0 scoreline after they were demolished at the Etihad Stadium on Sunday.
Sergio Aguero's treble saw the City striker draw level with Alan Shearer's record of 11 Premier League hat-tricks, with Raheem Sterling contributing a brace and Ilkay Gundogan also on target.
Chelsea trailed 4-0 after 25 minutes and Sarri told Sky Sports following the match that he expects to hold talks with the club's board over his future.
Guardiola, though, feels Sarri should be shown patience and drew parallels with his first season in charge of City, which saw the club fail to win a trophy.
"I know what he wants to do," Guardiola told a news conference after City leapfrogged Liverpool to reclaim top spot in the Premier League table.
"This kind of person, these type of games, the football helps to make it better. They beat us at Stamford Bridge [in December] and against Napoli last season [in the Champions League] it was tight, they were better in moments.
"But people don't understand how difficult the first year can be. People need time, [it] only depends on the owners, the people in charge need to believe.
"I came to Manchester City - the bosses, chairman, [director of football] Txiki [Begiristain], he knows me. He doesn't believe I'm bad when we lose and good when we win. That's why I'm enjoying it in Manchester. We were good in all aspects and that's why we won."
Sarri stormed down the tunnel without shaking Guardiola's hand at the full-time whistle, but the City boss said it was not an issue.
"I spoke with [Sarri's assistant] Gianfranco [Zola] and it's no problem," Guardiola added. "I have a good relationship with him."
David Silva was a surprise substitute for City with Bernardo Silva, Ilkay Gundogan, Fernandinho and the fit-again Kevin De Bruyne preferred in midfield.
"I need him, I miss him when he's not playing but I took the decision and try to be honest," Guardiola said of omitting David Silva, who came off the bench.
"Sometimes lately I don't play Kevin, Sergio, it's what I believe, I see the opponents, it's difficult. Dropping Gundogan is difficult, for the rhythm they have, Gundo and Kevin in that situation [were more suitable selections].
"But I need Silva as he's the best in the world in those small spaces, it's impossible to find it. But today I thought it was demanding, physically. It was a good decision.
"He played the last two games and was key. Especially in the second half at Goodison [Park, against Everton], we have a lot of games and we'll try to have everyone involved."