Ahead of the opener against Everton, Teddy feels that the Goodison outfit are one of the teams to look out for - especially given the impact made by the arrival of manager David Moyes last season.
The skipper is also very aware that there are never any easy pickings at Goodison Park.
"Not at all," he said. "Especially with David Moyes coming in and doing so well at the end of the season.
"I think with a lot of clubs below us last season, this time we're going to have to be in very good form to be in a high position really.
"There's clubs above us that are obviously good teams. But there is teams below us like Middlesbrough, Blackburn and then you come to the likes of Everton who looked very strong towards the end of the season under new management.
"They are all going to be looking to do better, obviously as well as us, so it could be a very tight season."
Teddy Sheringham warns that there are a clutch of clubs - including ourselves - looking good for an improvement on last term and predicts a particularly tight season.