Suarez scored a brilliant free-kick but was twice denied by Toffees goalkeeper Tim Howard in the second half of the 3-3 draw in which Daniel Sturridge salvaged a point for the Reds with an 89th-minute equaliser.
Gerrard knows the Uruguay international will not be thinking about his excellent personal performance - achieved despite a knee-high tackle from Kevin Mirallas which manager Brendan Rodgers branded potentially career-ending and could have resulted in a red card - or a point gained at Goodison Park.
"Luis is a machine. He's right up there with the best in the world," said the England captain.
"Luis is the type of player who won't be thinking about his free-kick after the game, he'll be thinking about the header he missed.
"That's why he's so good. He'll be desperate to get back out and make amends for that.
"That's what the best players do, they don't get big-headed over the good things they do but analyse the mistakes and where it went wrong and how they can improve."
Although Rodgers felt referee Phil Dowd got the Mirallas decision wrong Gerrard defended the official.
"To be fair to the referee when I initially saw the incident I was thinking 'yellow card'," he added.
"I was probably the same distance away from it as the referee so you have to give him the benefit of the doubt.
"Now I have seen it again though it's a red card, everyone knows that, but it's very difficult to say that in a split-second and at that distance.
"I think I'd rather back the referee than have a go at him."
- Sports & Recreation
- Kevin Mirallas
- Daniel Sturridge
- Brendan Rodgers