The 34-year-old passed up a number of set-pieces opportunities to his Italian team-mate throughout the derby as Liverpool pressed for an opener in the Merseyside derby.
He was letting Mario take a few [free-kicks] in the first half and I was screaming on for him to take it
However, Gerrard, who scored 13 Premier League goals last season, assumed set-piece duty in the 65th minute, producing a powerful free-kick which beat Tim Howard.
Everton captain Phil Jagielka levelled in injury-time with a brilliant finish of his own, and Liverpool manager Rodgers reflected on Gerrard’s second goal of the season.
“Stevie’s such a selfless guy,” said Rodgers.
“He was letting Mario take a few [free-kicks] in the first half and I was screaming on for him to take it, because he’s got so much quality.
“But he would rather, at times, let other people have an opportunity. He’s shown many a time over the years that’s his range. When he took it, it was a goal that should have won the game. But it was a wonderful free-kick and I thought his performance today was outstanding.”
MORE: Man United latest news
MORE: Arsenal latest news
MORE: Chelsea latest news
MORE: Liverpool latest news