Lambert, 45, has left Villa after the club slipped into the Premier League relegation zone.
In 25 top-flight games this season, they have managed just 12 goals.
“The club’s owner, Randy Lerner, warned me that I was embarking on the toughest challenge of my working life and he was not wrong,” said Lambert.
Aston Villa have scored twice in their last 10 Premier League matches
In a statement, the former Norwich City boss added: “But I have never stepped away from hard work and I put my heart and soul into the job from my first day until my last.”
Tuesday’s 2-0 defeat at fellow strugglers Hull City marked the end for Lambert’s 31-month tenure at Villa Park.
First-team coach Scott Marshall and goalkeeping coach Andy Marshall are now in temporary charge with 13 league matches remaining.
Former Spurs boss Tim Sherwood and United States coach Jurgen Klinsmann have been linked with the job on a full-time basis.
Lambert said he was “extremely proud” to have managed Villa.
“My initial remit was to conduct a massive overhaul of the playing squad, lower the overall wage structure of the playing staff and achieve this whilst keeping the club in the Barclays Premier League,” he added.
“There was also a concerted effort to purchase and develop younger players who would provide a solid footing for the football club to move forward and enhance the value of the playing squad in the future.”
Lambert, who was appointed in June 2012, said he owed “a great debt of gratitude” to many people at Villa, among them his coaching staff, Lerner and former chief executive Paul Faulkner.