The 30-year-old midfielder, on loan at Real Madrid, says that it will take time for new players in the squad to blend together as they attempt to replicate the glory years
The Blues are into the semi-finals of the FA Cup after defeating Manchester United 1-0 in Monday's quarter-final replay, and face Rubin Kazan in the quarter-finals of the Europa League.
And so while Essien concedes it is a season of change in west London, he insists they are still capable of salvaging a lost season with silverware.
"They can still win trophies in the cups this season so people shouldn't write them off just yet," the 30-year-old told The Sport Review.
"I have followed Chelsea all season, and although it hasn't been as planned at the start of the season, I think it's down to the fact it is a transitional season.
"A lot of the players from the past are not there and there are new players. It takes time to blend all of them and create a team straight away.
"I am sure the team will know each other very well and the good times will be back."
Essien also hinted he will be heading back to London after his loan deal in Spain comes to an end, stating that his contract situation remains the same as at the beginning of the season.
He added: "I have a contract at Chelsea and at present I am only on loan here [at Real Madrid], so nothing has changed."