Dirk Kuyt was the other scorer in a deserved 4-0 win - but it was Benayoun who Benitez singled out as an example of how those on the fringes can go on to play a crucial role.
The No.15 spent the first half of last season on the peripheries but is now a central figure at Anfield.
Benitez said: "We know he's a player with quality. We have seen how good he is coming from the bench and we were talking about whether he could start or not.
"Today he was very, very good and his movement was fantastic for the team.
"During the internationals I was talking with some players about how they could change things, and it was just to work hard.
"Yossi was away but he wanted to play, and when a player wants to play it's very easy: you have to prove these things in every training session and in a game if you get the opportunity.
"Yossi is someone with experience and he knows the best way to fight for your position is doing something well on the pitch."
Despite Benayoun walking away with the match ball, Benitez believes another player was key to the 4-0 victory.
"Lucas supported and managed in the middle and kept everyone else going forward," said the Spaniard.
"For me he was the key player today. We can talk about Yossi but it was thanks to Lucas. One thing everyone told me when I came here was that if you work hard the fans are with you.
"They could see again today that Lucas is a worker who has quality. He can challenge in the air, tackle and pass the ball.
"He worked so hard in different positions and allowed the other players more freedom. For me he was a very important player for us today."
On why Javier Mascherano was not in the squad, Benitez revealed the midfielder was still in South America after representing Argentina this week.
He explained: "Mascherano was not available. He still hasn't arrived. He is coming back on Sunday. He had some problems, and our doctor was talking to their doctor.
"Now I think he's okay but he's coming back later because he had to do some tests over there.
"Don't be worried, it's not serious!"
Burnley boss Owen Coyle reserved his praise for Steven Gerrard, who operated in a deeper role alongside Lucas.
"Steven Gerrard could play at right-back and still be effective because he is a world-class player," said Coyle.
"You see it on the international stage and the club stage every week. He's a real Liverpool player, I would say - though I would prefer it if he did play at right-back!"