Amid a difficult start to the season, 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 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," Lambert told the Liverpool Echo.
"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 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."
