The 35-year-old Ghana international believes the footballing world expects Jurgen Klopp's side to reach the final following an incredible run in the competition, notably the demolition of Manchester City in the quarterfinals.
Liverpool last played a Champions League final in 2007 under Rafael Benitez.
"They were a bit like the underdogs when they were facing Manchester City but they put up a good performance in both legs and qualified", Essien was quoted as saying by Insidefotbul.com.
"So I think they deserved to win and go through. Everyone including myself will be expecting them to go all the way," he added.
Liverpool will host Roma at Anfield on Tuesday April 24 before travelling to Stadio Olimpico for the return fixture on Wednesday May 2.