The Blues manager was under increasing pressure in his job after a poor run of form since the turn of the year, but an improved performance in their Carabao Cup final defeat to Manchester City on Sunday was followed up with a 2-0 win over third-placed Spurs at Stamford Bridge.
Pedro opened the scoring before Kieran Trippier’s own goal sealed the three points, while goalkeeper Kepa Arrizabalaga was dropped to the bench after his refusal to be substituted ahead of their penalty shoot-out defeat to City last weekend.
It has been a promising turnaround for Sarri, but Cole questioned his decision to go straight down the tunnel at the full-time whistle after beating Spurs rather than celebrate with the fans.
"I think things are sitting very well,” Cole told BT Sport.
"I think he could have been sitting here after defeat and we could have been having a very different conversation.
"But when you consider the situation the club were in last year he’s come in and steadied the ship, he’s got a great opportunity to make the Champions League and I believe would have been his mandate at the start of the season
"For a club like Chelsea to slip to the position they were in and have the furore that has happened for the last six months I think he’s steadied the ship.
"I think he’s done well. I think there’s still more to come.
"There was an opportunity today, you’ve just beaten your closest rivals, the fans were jumping, the players were celebrating with the fans, he should have been on the pitch with the players because then you can use that for the next game.
"There’s another level for him once he realises the culture and how important this game is for the club.
"On the front of it, there’s 10, 11 games and the Europa League so it’ll be important to balance the squads to make sure we win a place in the Champions League for next year."
