Villa have only won nine of their past 40 Premier League matches at Villa Park and lost 2-1 at home to Newcastle on Saturday.
Following their improved form at the end of last season and a victory at Arsenal on day one of the current campaign, expectations have been raised among the Villa fans.
But Lambert's men were booed off by the home support at half-time and full-time at the weekend, as they suffered a third defeat in a row.
Lambert told the Birmingham Mail: "I'd rather have that level of expectancy on our shoulders than not.
"It's important to have that to go and try and win games.
"It's too big a club not to have a big support, and it's thousands. You take the rough with the smooth.
"One thing I can never do is be critical of the Aston Villa supporters. They've been fantastic for us and, if you lose games, then you have to accept it, it's part of the game.
"I just think we've got to thrive on that crowd. It's a great crowd to play in front of and you have to be able to handle that."