The Uruguay international scored two for the second successive match as Sunderland were swept aside 3-0 last night.
Suarez has just two Reds trebles to his name, both against Norwich, but he has found net twice in a game three times on his way to 15 Premier League goals already this season.
"It's nice in a strange way that he hasn't had more hat-trick because he will want more goals," said Gerrard.
"Sometimes when forwards get hat-tricks they take their foot off the gas.
"I hope he's upset and went home angry that he only got two.
"With a game against Man United coming up hopefully he's saving a few for them.
"He's a warrior. It's very rare to see in a centre-forward that mentality, that they never give up and fight for every ball - even when you are 3-0 up.
"It's 'kids in the street' stuff. He's the same every day in training.
"The players in the Premier League are lucky they only have to test themselves against him twice a season.
"They should be very glad of that because he's running rings around us every day, all year round. We have to put up with it every day.
"I think he's already won goal of 2012 with the Newcastle one.
"Let's hope this one is up for goal of the year in 2013 and people don't forget about it because it came so early in the year."
Gerrard believes there are few to match Suarez on the current run of form he is in.
"He's just world class. There are a handful of players in the world who operate on a different level and he is one of them," he added.
"He can score all types of goals. I was looking in the programme at his goal record: for someone who the critics say doesn't score enough, just have a look at his record (Suarez has scored 31 in 64 league games)."
Forward Raheem Sterling is looking to learn from the likes of Gerrard and, more significantly, Suarez.
The 18-year-old scored his second Premier League goal against Sunderland and admits he should probably have had more this season.
"It was a good goal for myself, having been played in by Suarez," he said.
"You just have to work off Suarez and Gerrard and get into goalscoring positions.
"Luis is unstoppable. Day in, day out in training you can see what a good player he is.
"To play with him on match day is a dream come true and I'm looking to learn lots from him and take it into my own game.
"I thought I could have got a few more goals earlier in the season but as a young player you have to keep striving and playing a part in the team."
Victory over Sunderland kicked off 2013 positively for Liverpool, having struggled so much at Anfield the previous 12 months, and Sterling said confidence was high as they looked to achieve their targets in the second half of the campaign.
"We think we should play more consistently and nothing is impossible for us," he said.
He also welcomed the arrival of £12million new signing Daniel Sturridge.
"Daniel is a good player, a natural goalscorer, so to have another in the team there will hopefully be more chances created," he added.