"I have confidence we can beat anyone on a good day at Anfield. I would be worried today if the players hadn't worked as hard as they have," he told reporters.
"The fans will play a part, they'll push and will be behind the team," added Benitez after the last 16 first leg loss
Liverpool, whose latest setback followed Monday's 1-0 Premier League defeat at Wigan Athletic that left them sixth in the table, only have Europa League silverware to play for after early exits from the Champions League and FA Cup.
An attacking side - including Ryan Babel, Fernando Torres, Dirk Kuyt and Steven Gerrard - struggled with a poor pitch on a cold evening in the northern French town and were caught out late on by a fortuitous free-kick from Lille's Eden Hazard.
"Scoring a goal is nice and it was also very important not to concede one," teenage Belgium forward Hazard, who was a permanent danger, told French television channel Canal Plus.
"Now we know we must expect a tough match at Anfield but we will try to play as well as Lyon did against Real Madrid," he added, referring to the French side's success in knocking the Spaniards out of the Champions League on Wednesday.
Liverpool went close through Babel and a Torres header in an even match and Benitez was pleased with his team following their ninth league defeat of the season at Wigan.
"The attitude of the players was fantastic. We were talking about not letting the fans down in terms of team effort and I think we did this," the Spaniard added.
"Every game is important for us now. We have to be ready to play Portsmouth (on Monday) and try to win. Then we have to look to the Europa League game (with Lille), that is how it is when you are a top side playing in different competitions."
Five-times European champions Liverpool will welcome Lille to Anfield for the second leg on March 18.
