Lambert has found first-team action hard to come by at Anfield since his summer switch from Southampton, starting just five games in the Premier League.
But despite playing opportunities being limited, Lambert rejected the chance to move to Villa Park.
“I wasn’t aware of any interest until deadline day", he told The Liverpool Echo.
“I got a phone call from the gaffer about 4pm saying Aston Villa had come in. He said he didn’t want me to go but basically offered me the chance if I wanted to play football, which is fair enough.
“I spoke to my agent, I spoke to my wife, I spoke to Aston Villa and it was close. It was very close. It was touch and go. We agreed everything.
“The deal was agreed, but in the end, there just wasn’t enough time to say ‘yes’ – to make a decision in the space of four or five hours for the next two-and-a-half-years. Not just for me, but for my family as well.
“It was something I just couldn’t do. It was too short notice. It was too big of a decision to make in the short amount of time I had.
“It was something that I would have probably looked back at a few years down the line and regretted if I had moved too early. It was very close but I just couldn’t do it.
“It’s hard sometimes when you aren’t playing but I’m at the club I love. I’m not willing to give that up easily.
” Lambert also feels that Liverpool can make a real impact on the Europa League this season. Amid a difficult start to the campaign, Brendan Rodgers' side dropped out of the UEFA Champions League after a third-place finish in Group B alongside Real Madrid, Basel and Ludogorets.
However, with just one defeat from their last 16 outings, Lambert feels Liverpool are now a different proposition compared to when they crashed out of the Champions League.
"We'd been waiting for so many years to get into the Champions League so we were desperate to stay in it," he said.
"But we weren't playing well when the Champions League was there. If we'd just managed to sneak through, who knows what we would have been able to do now.
"Like I knew we were going to, we're playing at our best again now. We're in the Europa League and it's something that we'll be trying to win.
"You come into it at a good stage. I know it's not the Champions League but it's still a great competition."
Liverpool's improved form has seen them move up to seventh in the Premier League - four points off Southampton in fourth.
Lambert acknowledged that the Champions League spot afforded to the winners of the Europa League adds to the attraction of the competition.
"There is more prestige with a Champions League spot up for grabs," he continued.
"We’re trying to get into the top four, but we’re also desperate to win a trophy.
"If it’s not going to be both the FA Cup and Europa League then we’ll be trying for either one of them. If the added bonus is that you get a Champions League spot then that’s even better."