The visitors were held to a 0-0 draw at Elland Road despite playing most of the second half against 10 men after the hosts had Luis Sinisterra sent-off and the boss predicted some players would endure a sleepless night.
Ollie Watkins missed from close range after Philippe Coutinho hit the post and was then denied by goalkeeper Illan Meslier at the death.
Gerrard said: “When you concede goals you challenge your defenders. It is only fair I do the same to those in the front half of the pitch. We need our big players to step up.
“We played well today. We knew it was going to be tough. A point before the game would have been OK. It is a tough place. But how the game panned out, it is not enough. The game was there for us. One or two of our players might not sleep as much as they should have done tonight.
“The sending off was helpful. After that we have to go and take the game.”
Watkins was twice denied by Meslier in the first half, while Coutinho and substitute Emi Buendia also shot narrowly wide.
The draw extended Villa’s unbeaten run to three matches and Gerrard continued: “Disappointment is probably a bit too strong but certainly frustration. That is a big chunk of the second half (playing against 10) and over the course of the game we have created enough to take three points from the game.
“We have asked for a big improvement in terms of our final third play and I think that was clear for everyone to see.
“But you have to take those chances and those moments. If you do, we would be much happier with our league position.
“I think we have the quality. We are doing tonnes and tonnes of work in those areas.”
Gerrard, meanwhile, fears Ludwig Augustinsson could be set for an extended spell on the sidelines after being forced out of his Premier League debut before half-time with an apparent hamstring injury.
The Sweden international will undergo a scan today and the Villa boss said: “When you leave the pitch as early as that, holding that area, you fear the worst.”
In better news, Matty Cash and Calum Chambers were due to return to training today, the latter missing out yesterday after undergoing minor surgery on his appendix.