The Northern Irishman watched on as his side signed off their impressive league campaign with a 2-1 win over Newcastle United at Anfield on Sunday.
However, the victory was not enough to steal the title away from Manchester City, who won 2-0 at home to West Ham to claim their second Premier League crown in three years.
Despite the disappointing end to 2013-14, Rodgers is insistent that the club now hold the belief that their long wait for a league title will be brought to an end soon.
"The word now is belief," he said. "Belief that we can be up there challenging.
"I read a letter to the players on the first day of the season from a supporter, who told us about getting into the top four and the pride he has in the club.
"And not just to think about fourth but to think of winning.
"Probably at the same time the players and maybe the staff thought the letter was maybe a bit far-fetched.
"I read the same letter back again (on Sunday) and all the words that went into the players' minds were the same as the beginning.
"It's been a wonderful campaign. The overriding feeling at the moment is one of sheer pride of the players.
"It's been incredible to see the supporters, we've made them dream and that's our job to do that. And the great thing is, we'll improve."
