However, there is a cautious optimism about the squad manager Gareth Southgate has moulded for Russia with a young team desperate to showcase their talent on the global stage.
And Tottenham midfielder Alli, a key component of Southgate's team, called on England to show a killer instinct.
"We know we have to be ruthless. It's international football. You are not going to get too many chances, so when they do come you have to be ruthless and put it in the back of the net," Alli told The Evening Standard.
"We are going to have to be patient. Tunisia defend very well, so if we do have a lot of possession we have to make sure we are not forcing it. We have to stick together as a team."
England have not won a knockout game at the World Cup since 2006, a narrow round-of-16 win against Ecuador, but are tipped to progress out of Group G where they are expected to tussle with Belgium for top spot.
While expectations for England's campaign are perhaps lower than in previous tournaments, Alli insists the squad believes they have the capability to go all the way.
"I don't think we can put a limit on what is possible for this tournament. We don't want to say we can only get to the quarters or semi-finals," the 22-year-old added.
"We believe we can go all the way. We have to. There is no point coming here and believing anything else."
England follow up their opener with a clash against tournament minnows Panama on Sunday, before finishing their group fixtures against Belgium.