United were installed among the relegation favourites following promotion from the Championship in 2019 before defying the odds to secure a top-half finish.
Chris Wilder’s Blades began the new campaign with a 2-0 home defeat to Wolves and will look to bounce back at Aston Villa on Monday evening.
Defender Egan, who has played a key role in the South Yorkshire side’s remarkable rise, is unconcerned by suggestions the team may struggle to replicate the achievements of last term.
“All I hear about is second season syndrome, getting asked that. But as a player you don’t even think about it, it doesn’t even cross your mind,” said Egan.
“I am sure that is the same for the rest of the players here.
“You just look forward to the next game, in the Premier League you can’t look too far ahead or you can’t look behind you because the next game is the most important game.
“Every team in this league is a really good team. It’s the best league in the world for a reason so you have to prepare really well for every game.
“Last year we came up and everyone was saying, ‘you’re going to go straight back down’ and we ended up finishing ninth, which was brilliant. But that’s done now. A new league has started and we’ve got a big game Monday.
“If you start setting yourself targets and looking too far ahead it could come back to bite you.”
Republic of Ireland international Egan looks set to go head-to-head with former team-mate Ollie Watkins at Villa Park.
Forward Watkins, who played alongside Egan at Brentford, is poised to make his league debut for Villa following a club-record £28million move.
Centre-back Egan insists personal relationships will be put aside as he attempts to prevent his friend from following up a Carabao Cup goal at Burton with a memorable maiden appearance in the top flight.
“He was there when I was there so I get on quite well with Ollie. He did really well at Brentford, really well last season, after changing to a striker,” said Egan, who signed a new four-year contract at Bramall Lane last month.
“Hopefully on Monday we can keep him quiet and then he can do what he wants.
“Whether you are playing against someone you know, or you don’t know, the goal stays the same – work and try and get three points.”
Blades boss Wilder is chasing another striker before the transfer window closes but does not expect to bolster his options before taking on Dean Smith’s side.
He remains without French forward Lys Mousset because of a toe injury.
