A 2-1 home defeat by Olympique Lyon on Tuesday left Liverpool third in Group E after three games, six points behind leaders Lyon and three behind second-placed Fiorentina.
Frustrated supporters turned on Benitez at Anfield after a fourth successive defeat in all competitions, Liverpool's worst run for 22 years.
On a bad night for the Premier League club, captain Steven Gerrard lasted just 24 minutes in his comeback game from injury before he limped off.
The England midfielder is now a major doubt for Sunday's home game with Premier League leaders Manchester United, a match Liverpool have to win if they are to maintain a realistic chance of challenging for the title.
"I think it is something we are going to have to do," said Benitez, when asked if Liverpool would have to win their remaining three group games to stay in the Champions League.
Benitez takes his side to Lyon on Nov. 4 before facing Hungarian side Debrecen away on Nov. 24. They round off the group campaign at home to Fiorentina on Dec. 9.
"I wanted to use some fresh legs," Benitez explained after his decision to replace goalscorer Yossi Benayoun with Andriy Voronin was met by a chorus of boos from supporters.
"The fans know Yossi is a good player but he was a little bit tired.
"It's a really disappointing outcome.
"We had too many problems before the game with injuries.
"But we still managed to take the lead and we still managed to create chances."
Benitez refused to rule out Gerrard for Sunday's game with United but Spanish striker Fernando Torres has missed the last two games and remains doubtful.
"We need to lift ourselves for Sunday, it's something we have to do," added Benitez.
"We have to push the players and have to keep going. Had we taken our chances against Lyon then things would have been different."
