Lambert left Villa Park 24 hours after a defeat to Hull City that saw them slip into the Premier League's bottom three, with the former Norwich City boss describing the job as the toughest challenge of his career.
The Scot claimed financial restraints saw him struggle to build any sort of momentum with his side, but director Krulak dismissed the suggestions.
"Paul was just not bringing the team together," he told The Sun.
"Randy was loathe to remove a manager mid-campaign, but there was this intensely strong feeling, not least from the players and fans, that Villa should be doing a lot better.
"Randy wants a team that - win, lose or draw - is fun to watch. But the opposite was true.
"This idea that Randy had not put money into the club and that Paul's hands were tied is simply not true. It's hogwash."
Villa's woes have been underscored by their abysmal form in front of goal, which has seen them score just 12 times in 25 league matches.
They face Leicester City in the FA Cup fifth round on Sunday, when first-team coach Scott Marshall and goalkeeping coach Andy Marshall will be in temporary charge.
