The Foxes have managed to stay on course to finish in the top four in the league for the majority of the season with big wins over champions Liverpool, Chelsea and Manchester City along the way.
Leicester sit in third place in the top flight table with 56 points and are one step closer to claiming the FA Cup after beating Southampton in the semi-finals on Sunday.
With Leicester enjoying a strong run in the domestic competitions this season, Rogers has called on his team to finish the job in the Premier League and deliver FA Cup glory to Foxes faithful.
The former Celtic boss asserted that Leicester want to challenge for trophies with his side also mounting a consistent challenge in the race for Europe.
“It’s not just the team, it’s everyone working here”, Rodgers told Leicester’s official site.
“They’re all connected to the success.
“But what is important is that you can’t be comfortable with it. That was my point. The club is over 50 years since it’s been to the final, which is amazing, but when that comes, we want to win it.
“You don’t soften up.
“We want to be here, we want to be challenging.
“That’s what I said when I came into the club.
“We set our base at this club towards the summit of this league so that we can challenge and fight for honours.”
With seven games left to play for them in the league, Leicester will look to grab maximum points to secure a spot in Europe.