Hodgson was drafted in to the role at the 11th hour after 18 months in charge of West Bromwich Albion.
Prospects have in the past been high for England heading into international tournaments.
However, in the build-up to the European Championship, these have since lowered with many believing that reaching the knockout stage of the competition will be considered a success.
As such, Keegan believes the 64-year-old will benefit without the added pressure that has been shouldered by his predecessors.
"The expectation level has been dampened a bit and with a new manager coming in so late, people are accepting it [winning the tournament] might not happen," Keegan told Yahoo!
"Which is a complete change but that might be to England’s benefit; only time will tell. But you can see England getting into the semi-finals and people saying we’ve done really well, where as normally if we don’t win it, we’ve failed.
"This squad is going in with a lower expectation level and with things like [Wayne] Rooney not being able to play for two games, its been dampened.
"But Roy Hodgson and his staff and the players might benefit from that and they may surprise people."
The inclusion of Arsenal winger Alex Oxlade-Chamberlain was one of the surprises of Hodgson’s 23-man squad, with the youngster having played only a handful of domestic games for the Gunners.
And Keegan feels the 18-year-old has the potential to be the surprise package of the tournament.
"I don’t think he’ll feature prominently, I think he’s going there as someone you can just throw on late in the game, for experience, that’s why I think he’s going," he added.
"But like I said he could go on with twenty minutes to go, score a goal, change everything and be the star of the show. That is the beauty of football, not just playing for England.
"He’s only played twelve times for Arsenal, which is nothing, he had one very good game against Milan, and it’s not easy to play against Milan but it is only one game.
"So he is very short on experience and he’s got to learn a lot, but he is obviously the one player that Roy Hodgson wanted to throw in to inspire all the other youngsters and make them say, it could have been me.
"Alex won’t even be nineteen when the tournament is finished, so I think it’s been a clever one. He has not taken him as a key player but as a surprise package."
For more insight from Kevin Keegan and other leading managers, plus coverage of Euro 2012, visityahoo.eurosport.com
