After last season saw manager Sam Allardyce come in for criticism over the team's style of play, West Ham have recruited former striker Sheringham in a bid to provide the attacking brand of football the Upton Park faithful crave.
Hammers fans were dismayed by Allardyce's tactical approach but despite the unrest, Sullivan, co-owner David Gold and vice-chairman Karren Brady opted to back their manager.
Sullivan believes offering such support to Allardyce quashes suggestions the club are dictated to by opinions from the terraces.
“It's quite the opposite,” he told the Daily Mirror. “They voted 80-20 per cent to sack the manager. We didn’t sack the manager.”
West Ham get their 2014/15 campaign underway on August 16 as London rivals Tottenham visit Upton Park and Sullivan admits the fans are right to be ambitious.
“You can’t just look to stay up,” he said. “It is not acceptable to our supporters to say, ‘We’ve survived. We’ve had a very good campaign'.
“We are not Norwich. We are not Fulham. We are not Reading. We are West Ham United.
"Our supporters are realistic. They know it is a huge and difficult task to break into the top six. But we must be aiming for that, even if we don’t achieve it.”
Sullivan believes the addition of former England forward Sheringham to the coaching staff will prove influential, but denies suggestions the appointment undermined Allardyce.
“We had a lot of people approach us to become our attacking coach and Sam picked the one he wanted,” he added. “Yes, we suggested the idea, but Sam liked it.
“We didn’t undermine him at all. I think he has analysed the performance of the team last year and agreed that we would like to score more goals. It was a weakness of the team and he has brought in an expert to try and improve that.
“Teddy has played at the highest level. If you combine his game intelligence with the level he has played at, I do not believe that he won’t improve our attacking ideas, whether it is the way we take our corners, our free-kicks, or just our overall strategy.
“I believe we will be a better team for having him as part of our management set-up.”