Liverpool took a 2-0 lead inspired by striker Luis Suarez, who created the first and headed home the second, before Everton physically overwhelmed the visitors at the end of the first half and clawed back level before the break.
Suarez had an injury-time effort harshly ruled out for offside and Liverpool finished the day as they began it - six points behind Everton in the Premier League.
"Every single time they get the ball to the goalkeeper it comes in long," Gerrard was quoted as saying by the BBC on Tuesday.
"There was only one team who came to play football and that was us. Everton are not better than us."
Possession statistics after the match showed Everton had actually enjoyed the greater share of the ball and completed more passes than Liverpool.
"I thought we were fantastic and stood up to a team that are very similar to Stoke," Gerrard added.
"Everton are effective because they have some big, physical lads in the team. We had a young, small team out there who were men and stuck together."