Fourth-placed Tottenham are two points ahead on 64, with a match in hand, and Liverpool must win their remaining two games and hope neither Spurs, Manchester City nor Aston Villa amass more than 68 points.
"I think we have a chance so we will try," said Benitez on seventh-placed Liverpool's chances of finishing fourth. "We know they (Tottenham and City) still have one game in hand but we are close and we will try our best."
He added: "Maybe the best results for us is for them to draw and then if we can get six points we will have to see.
"If we finish on 68 points we will have a chance because we will have better goal difference."
Two goals from captain Steven Gerrard, a maiden Liverpool strike for Maxi Rodriguez and a late effort from Ryan Babel relegated Burnley from the Barclays Premier League on Sunday.
Gerrard's first goal in the 51st minute was deflected off Burnley centre-back Leon Cort but his 25-yard strike seven minutes later was inch-perfect before Rodriguez and Babel wrapped things up.
Benitez was pleased to see his captain back on the scoresheet and Rodriguez finally opening his account after his January move from Atletico Madrid.
"Stevie needs to score, it was good for him and good for the team," said the Spaniard.
"Maxi has had some chances in the past and now he has scored it will be good for him too."