The Italian giants have won just one of their seven league fixtures in 2015 – falling to 11th in the table as a result.
A home fixture against relegation-threatened Cesena on Sunday gives Filippo Inzaghi's men an excellent chance to reverse their slump.
But defeat could be disastrous to the mood at San Siro - something that Essien is aware of.
The midfielder emphasised the importance of a united squad and told the club's official website: "We are in a difficult time [but] we have to stick together and try to change the situation.
"We are trying to do our best. These moments happen in football, we cannot let our heads drop.
"We have the quality to get out of this crisis. We are working hard to improve.
"We need them [our fans], but it is normal that they are not happy… [we want to] make them smile again.
"Against Cesena we have to be positive... and try to win the game."
Milan were held to a 1-1 home draw against Empoli last time out - Massimo Maccarone netting a second-half equaliser for the visitors.
Goalkeeper Diego Lopez was sent off with seven minutes to play and will be suspended for this clash.
Without a clean sheet in nine matches in all competitions, it is a further blow to Milan's defence.
Inzaghi will at least be encouraged by Mattia Destro's goal against Empoli.
The forward, who joined from Roma in January, is desperately needed to revive a Milan side so reliant on the goals of midfielders Jeremy Menez (12 Serie A strikes this term) and Keisuke Honda (six).
Cesena may sit 19th in the table, seven points adrift of safety, but they will be encouraged by a 2-2 draw with champions Juventus last Sunday.
Franco Brienza's equaliser with 20 minutes to play capped an impressive performance from Domenico Di Carlo's side.
Cesena have shown recent signs of improvement, beating Parma and Lazio in the last month, and a win at Milan would present a major scalp.
Milan have not lost to Cesena since September 2010, but were held to a 1-1 draw on the road earlier this season.
