The Uruguay international was at his brilliant best with a 30-minute first-half hat-trick before adding a trademark 25-yard free-kick after the break and then laying on the pass for Raheem Sterling to score late on after Bradley Johnson's consolation for the visitors.
Manager Brendan Rodgers felt the performance edged Suarez closer to the likes of Barcelona's Lionel Messi and Real Madrid's Cristiano Ronaldo and Allen could not disagree.
"That's what you call a masterclass," said the Wales international, who made his first home league start of the season.
"Luis showed why he's one of the best players in the world. There are not many teams in the world who would be able to cope with that kind of performance.
"He was unstoppable. It was fantastic from him individually and for us to get three points after the disappointment of the defeat to Hull (on Sunday) was vital.
"We were lucky we had the chance to get back out there just a few days later.
"We all wanted to get back to winning ways and back to performing in the way we know we can.
"Luis takes the burden off a lot of the players when he scores goals like that.
"He inspires everyone and it's a pleasure to work with someone of his quality.
"He is getting more and more consistent and that's fantastic for Liverpool Football Club. Long may that continue.
"When you have a player of that quality in your team you want to keep hold of him for as long as you can.
"At times it's just a case of getting the ball to him and letting him produce. His goals came out of nothing really."