Liverpool head into Sunday's visit of Tottenham following Wednesday's 2-1 success over Sunderland, a victory that left Rodgers' side just one point behind Premier League leaders Chelsea.
The Merseyside club have won their last seven league games, but that run has not prevented Sherwood from questioning Liverpool's ability to challenge Chelsea and fellow title rivals Manchester City.
However, Rodgers has been quick to dismiss Sherwood's comments, insisting that his players are calm ahead of the final run-in.
"We're very relaxed," the Northern Irishman said. "We're focused. There was no expectation on us being where we are, so there's certainly no pressure."
Rodgers also hit back at Sherwood, indicating that Tottenham - who sit seven points adrift of the top four in sixth - have performed below expectations this season.
"I suppose the likes of Tottenham are a team who were maybe looking to be challenging for the league this season. You spend £100million-odd - it's a group that's set up to challenge," he added.
"There's certainly no pressure on ourselves, and I think we've shown that over the course of the season. We're playing with no fear.
"We're very hungry to succeed and that can give you a real advantage. We've proved that already this season. Experience isn't everything.
"We're looking to make sustainable success. That's our objective. We're looking to build something here."
