The Scot was sacked on Wednesday with the Midlands club in the relegation zone and in freefall and questions being asked about the club's policy in the transfer market.
American owner Randy Lerner's reluctance to sanction expensive signings means Villa have promoted through the youth ranks and signed players from lower division -- an admirable policy but one which is fraught with danger.
"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," Lambert, whose side managed only 12 goals in 25 Premier League games this season, said in a statement.
"My remit was to conduct a massive overhaul of the playing squad, lower the overall wage structure of the playing staff and achieve this while keeping the club in the Premier League.
"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."
Villa have been one of the lowest spenders this season and in the January transfer window added only young Valencia striker Carles Gil to their ranks with Scott Sinclair joining on loan from Manchester City.
Before the season they signed left back Aly Cissokho and midfielder Carlos Sanchez with the likes of former Chelsea forward Joe Cole and former Arsenal defender Philippe Senderos joining on free transfers.
Lambert's cause has not been helped by the poor form of striker Christian Benteke while former Manchester United and England midfielder Tom Cleverley cannot even get a game.
Former Villa player Paul Merson said Lambert should not take all the blame for the club's perilous league position.
"You've got to spend money and if you spend money you've got a chance," he told Sky Sports.
"If they get 10 million pounds they buy four or five players at a million-and-a-half each, -- that's not enough. This league is very, very difficult and you just can't get by."
(Reporting by Martyn Herman, editing by Pritha Sarkar)
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