The forward struck twice to take his tally for the season to 17 goals in 11 games, just a matter of months after demanding to leave the club.
The Uruguayan took his tally to 17 goals in 11 games with Liverpool's first and fourth in its biggest ever win at White Hart Lane.
Gerrard called his teammate the "best player in the world" and acknowledged it may be difficult to keep him at Anfield.
"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."
One thing that could keep Suarez in red, said the England midfielder, is securing European competition.
"Luis is the key to [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," Gerrard said. "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.