Bukayo Saka’s 30th minute strike earned the Gunners a 1-0 win at Villa Park which strengthened their bid for a top four finish.
Though Villa hit the post through Ollie Watkins, they didn’t manage a shot on target until the final kick of the game and Gerrard took issue with his team’s first half showing.
He said: “We waited. We waited to go a goal behind and then we got a reaction from the players collectively.
“I thought we were too passive and too respectful to the opposition for 45 minutes.
“We didn’t deserve anything with our first half performance. I thought we were second best.
“Arsenal played really well and controlled a lot of the first half. We had too much respect and lacked belief in ourselves collectively.
“It wasn’t until the game got into the second half we looked anywhere near where I wanted it to look.
“We have no complaints on the overall scoreline. We could have snatched something at the end when we were a bit more positive.
“It was a big improvement and a lot more like us but we didn’t start well and were really frustrated with our first half performance.”
Defeat left Villa ninth in the table and with a 10-point gap between themselves and eighth-placed Wolves, their current position is probably the extent of their ambitions with nine matches remaining.
Philippe Coutinho finally forced Arsenal keeper Bernd Leno into serious action with a free-kick deep into stoppage time.
Gerrard continued: “Of course, we need to have respect. The kind of run Arsenal are on and how much they have improved. Mikel Arteta has done a fantastic job.
“But if we have any ambition from the top to the bottom of the club, when we are at home we need to go and grab these performances, these positions of people above us in the league who have been above us for a long time.
“The first thing you need before a ball is kicked is everyone really believing we can. I certainly do.
“When we are at home, we need to at least believe collectively we can take points off these teams.”