The Uruguayan took the captain's armband in place of the injured Gerrard for their trip to Tottenham on Sunday and inspired them to a comprehensive 5-0 victory.
Suarez took his tally to 17 goals in 11 games with Liverpool's first and fourth in their biggest ever win at White Hart Lane.
Gerrard labelled his team-mate as the "best player in the world" and acknowledged it may be difficult to keep him at Anfield unless they can return to European competition for next season.
"He is relentless. He doesn't give up no matter what the scoreline is," Gerrard told Sky Sports.
"He's always chasing defenders back and he wanted a hat-trick. In the 90th minute he is trying to get his third goal and that just sums him up. He never gives up.
"We're lucky to have him and we need to enjoy him while he's here because if he keeps performances up like this, I hate to say it but the big guns are going to be sniffing, which is what we don't want.
"Luis is the key to that (UEFA Champions League qualification). If he can stay in this form and keep producing performances and goals like that, there is no doubt we will finish in the top four.
"That's what Luis wants and that's what he deserves. He deserves to be in the Champions League. A player of that quality has to be in the Champions League."
Jordan Henderson, Jon Flanagan and Raheem Sterling also got their names on the scoresheet against Tottenham as Liverpool moved back into second place in the Premier League.
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