The Midlands club have returned to the top flight after a decade in the lower divisions and face a tough opening fixture at home to Everton on Saturday.
They then face Chelsea, Arsenal and Manchester United in three of their subsequent four games but Morgan, who signed a new three-year contract this summer, says his side are quietly confident of survival.
“We look at our fixture list and it’s obvious we don’t have the easiest starts to the season,” Morgan told Sky Sports.
“But we’ve got to stay confident in our ability - that’s the key to staying up - and we know we’re more than capable of doing well.
“We understand the Premier League is a completely different ball game, playing up against some of the best players in the world, but if we focus on our jobs and re-ignite the form we showed last season then we know how good we can be.
“Consistency is essential. We might not get some of the results we want but over the course of the season if we are consistent in our performances we ought to get the ones we want more often than not.”
The omens are positive for Leicester, with two out of three promoted sides managing to survive their first season in the Premier League for the last five years.
And Morgan, who joined from Nottingham Forest in 2012 and has never played in the top division, said manager Nigel Pearson will not simply set his team out to be difficult to beat.
“We’ll approach each game differently, he’s got different tactics which will depend on the team we play,” Morgan said.
“It’s been a good pre-season. We’ve done well and we’re quietly confident. First things first we’ve got Everton and it’s not an easy league.
“I can’t wait from a personal point of view. This is my first season in the Premier League and it’s something I’ve waited for my whole career. I’m raring to go. “
Wes Morgan was speaking exclusively to Sky Sports at the Premier League launch event at the Capital City Academy in London.