The 32-year-old - a boyhood Liverpool fan and former Anfield trainee - completed a move to Brendan Rodgers' side in June for an undisclosed fee.
Liverpool are 4/11 with Bet365 to beat Southampton on the opening day of the Premier Leage season
That form prompted a call up to the England squad for the World Cup as well as a bid from Liverpool, but Lambert is now keen to focus his attention on performing well for his new employers, rather than focusing on the past.
"It's gone," he told Liverpool's official website. "I'm thinking about training sessions now and trying to do my best to get fit.
"Obviously I'm still made up to be here but it's gone. It's about knuckling down now and doing my best.
"I went back early so I met the lads that I hadn't met before and was around them for a week before the England lads and other internationals came back.
"I've been here for four weeks and I feel at home. My family are settled and already in a house, so I don't need to worry about them - I can just concentrate on football."