The 28-year-old Netherlands international, who scored a wonder-goal on the last day of the season, believes Lambert's youthful side will continue to grow with experience
Villa finished the campaign in 15th place, five points clear of the relegation zone. For a time it looked as though the Midlands club could drop into the Championship, but a good run that included a 6-1 win over Sunderland saw them safe.
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"It has been a good experience for all of us," he told the club's official website. "I am really looking forward to the new season because in the last few months we have really shown what we are capable of.
"We have a young team but the experience from this season we will take into next the next, I really look forward to it.
"You only want to look up. When pre-season starts, we look to our first game and we will look to do better.
"In the past few months we have really shown what we are capable of. We did a lot better. We stepped up and got really good results especially against the teams around us. We only lost against teams at the top, I think we did really well.
"We learnt a lot through the season, for many of us it was our first in the Premier League. We have good momentum, we all know what we can do, we can play good football."
Vlaar joined Villa from Feyenoord last summer, and has two years remaining on his contract.