The Saints are currently 18 points behind fourth-placed Arsenal with seven games left to play.
Despite their slim chances of qualifying for the Champions League this term, Lambert believes that Southampton will climb the table in the coming seasons.
"Our desire is to get into the top four and that's the way the club has been run in the past four years and that's the vision the players have and it's the one that the club has," the England international told the club's official website.
"So for me it's what the players still want going forward and it's what we're expecting to be honest."
Southampton return to Premier League action on Saturday at home to Newcastle United.