Dean Smith is the new man in charge at Villa Park (Image: GETTY)
Steve Bruce was recently relieved of his duties (Image: GETTY)
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"But the expectancy level was really really high, always.
"Dean Smith is going to have to master that side of it."
Lambert spent three years at Villa before being sacked in 2015 with the club 18th in the Premier League table.
The Scot was replaced by Tim Sherwood but he was unable to stop Villa finishing rock bottom, 17 points off off 19th-placed Norwich.