The club were promoted to the top flight in 2014 and won the Premier League title in 2016 before their owner died in a helicopter crash last season.
Rodgers was appointed in February, replacing Claude Puel, who was sacked after 16 months in charge.
“I don’t think we had a Premier League identity,” said goalkeeper Schmeichel.
“We had an identity in the Championship, the way we played under Nigel Pearson for three years. Then we came up to the Premier League and we had the great escape season, then winning the Premier League in our second season.
“But then you’re floating around thinking ‘what kind of team are we?’
“We skipped a few steps. It’s really important now we find that identity – who are we and what kind of team are we.
“Everything is in place; we have an amazing manager, amazing owners, a new training ground and everything is there to establish ourselves.
“When you look at the squad, the potential, the youth, the chances are endless. We are a club that believes in the impossible and want to establish ourselves as one of the top clubs.”
Rodgers, who joined Leicester from Celtic midway through last season, said he wants his team to play “exciting and entertaining” football “in a way that improves players”.
The 46-year-old Northern Irishman took over with the Foxes 11th in the Premier League, and led them to a ninth-place finish.
After supporters’ complaints about the style of football under former boss Puel, Schmeichel said Rodgers’ arrival “raised everything a little bit”.
Rodgers added: “Culture is very important, culture is half the battle. If you can create an environment where players come into work you can create a code in your work and then you live by that every day, that’s absolutely key. Running alongside that is a playing identity.
“I have an inherent belief in the way I work. It’s not the right or wrong way, but it’s how I’ve always perceived development of players and how I want my teams to perform.
“Ultimately we are here to win but we want to win in a way that excites and entertains supporters and in a way that players will improve.
“Building that culture and environment is something we have put a lot of work into and something that will continually grow the longer work together.”
“His identity is imprinted on this club wherever you go,” the Danish goalkeeper said. “All his values, everything he was about, we are about: family, togetherness, unity, courage and making the impossible possible.
“He was nicknamed ‘the impossible man’ and he had a belief. You could doubt it but when you looked him in his eye, you were in no doubt that he meant what he was saying. When a man like that says that, he gives you belief and his loss will always be felt within the club.
“Luckily we have his son [Aiyawatt]. The way he has stepped up and dealt with unbearable grief and not tried to hide it, but to share it with fans and to lead the club, we are lucky.”