Despite the Toffees being six points and seven places above them Gerrard insisted David Moyes' side were not the superior team in the city.
"I thought we were fantastic and stood up to a team that are very similar to Stoke," said the 32-year-old. "Every single time they get the ball to the goalkeeper it comes in long.
"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.
"There was only one team who came to play football and that was us.
"Everton are not better than us."