The Saints have been the surprise package in the Premier League so far, climbing up to third place in the table with six wins from 11 games.
Despite their good form, Lambert is confident that the South-Coast outfit can stay consistent.
"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 (beating Hull City 4-1), that's gone and we had to do it all over again.
"That's where the determination came from in each and every player by the gaffer to keep on pushing, keep on improving, don't just stand still."
Southampton continue their Premier League campaign on November 23 when they make the trip to Arsenal.