The newly-promoted Foxes host Everton on Saturday before playing Manchester United, Arsenal and Chelsea in their opening five fixtures.
"It's probably the toughest start you can have. Nobody's expecting us to win those games so any points out of them will be bonuses. Let's see where we are after that," Nugent told The Independent.
"If we're struggling we could be in for a long, hard season, but if we get a few points I think we can surprise a few teams in the Premier League."
Nugent, who scored 20 goals last season, recently signed a new two-year deal with Leicester.