England will play all their group games at Wembley, with potential matches in the last-16, semi-finals and final also being held at the national stadium.
The Football Association has targeted a capacity of 22,500 fans for its group games and last-16 ties, and is looking at an attendance of 45,000 as a minimum for the semi-finals and final.
"It's not going to be easy," said Robinson, who won 41 England caps between 2003-7. "It's not going to be a foregone conclusion as the bookmakers think it might be, I think there's some really tough opposition.
"But what is going to help is that the majority of England's games are at Wembley and the fans are going to be back in the stadiums.
"So if we can create that Euro 96 feeling, get people throughout the whole country behind the team, then yes, they have a fantastic opportunity to win it."
The tournament, delayed a year because of the coronavirus pandemic, will be held across 11 hosts cities throughout Europe.
England lost on penalties to Germany in the semi-finals when they hosted Euro 96 and Robinson urged caution when assessing the current opposition.
"I think they've got an outstanding chance," the ex-Leeds and Tottenham keeper said. "You look at the squad and the talented players, but it's very difficult.
"People get carried away. The expectation in this country is always high.
"I think defensively they've got a few issues, the final two thirds of the field I feel they've got the attacking talent to rival anyone in Europe.
"But you've got to take into consideration the teams they've got to beat along the way, I think people sometimes get blinkered and just look at the England team.
"You forget about the world champions France or the number one team in the world Belgium and then the Italians under (Roberto) Mancini, they haven't lost in over 20 matches.
"There's a lot of potentially tough games and you've got Portugal, Spain to throw into that mix."
* Robinson will be alongside presenter Simon Thomas and Lee Dixon when Amazon Prime Video broadcasts Brighton's Premier League game against Leeds on Saturday at the Amex Stadium.