The Saints are currently in fourth place in the Premier League table thanks to four wins from their opening seven fixtures.
Despite their positive showing so far, Lallana stresses that he and his teammates are keeping their feet firmly on the ground.
"We'll just take it a game at a time," he told the Daily Echo.
"For however long we're in fourth we're going to want to stay there and look up, we're not going to look behind us. That's the same as any team."
Southampton return to league action on October 19 when they travel to champions Manchester United.