The England international believes there is more to come from the high-flying Saints, who sit third in the table having garnered 22 points from their first 11 matches
Mauricio Pochettino's men sit third in the English top flight, three points behind leaders Arsenal, and have lost just one of their opening 11 fixtures.
However, England striker Lambert insists the squad is not content with standing still and will look to improve with every performance.
|17/1||Southampton are 17/1 with Paddy Power to finish in the top four|
"You're always worried about complacency, but we were determined not to let that sneak in," he told the club's official website.
"We want to improve every week and, even though we played so well last week [in a 1-1 draw at Stoke City], that's gone and we had to do it all over again [when beating Hull City 4-1 on Saturday].
"That's where the determination came from in each and every player to keep on pushing, keep on improving, don't just stand still.
"There are a lot of remarks made from a lot of people, but I don't think we've been too bothered about them for the last four years and we're certainly not going to be looking at any headlines now because what we're driving for is to do well for ourselves and anyone who writes anything - it's up to them.
"We know what we're trying to do and we have the belief and determination to do it."
Lambert, along with Southampton team-mates Adam Lallana and Jay Rodriguez, is part of the England squad to face Chile and Germany at Wembley.