The Foxes concluded the 2018/19 campaign with a 0-0 draw against Chelsea at King Power Stadium earlier in May, confirming a ninth-placed finish in the Premier League.
Following Rodgers' appointment in February, City won five and drew two of their 10 matches, scoring 17 goals and conceding on just eight occasions.
Leicester's 3-0 success over Arsenal, meanwhile, was among the highlights of Rodgers' early tenure - and Elliott says they can build upon that performance next season.
The former Foxes defender, 50, has watched closely over recent weeks as part of his duties for LCFC Radio's Pre-Match Pint and Matchday Live shows.
"As usual there’s been plenty to talk about and report on at Leicester City," Elliott told LCFC.com at the end of the Club's fifth successive Premier League season.
"They started the campaign well enough and it was a period of transition. That progression was there, but it started to falter a little bit over the winter.
"There were performances which were excellent. I’m thinking about Chelsea, Manchester City, Everton, Liverpool… against the big sides, the tactics were working.
"Against Arsenal it was different, they were totally dominant and we saw Brendan's methods in action. It was brave, bold football which bodes well for the future."
As the Club prepares for the 2019/20 campaign, Rodgers and his talented squad will be confident of building upon the progress they've already made together since late February.
Elliott believes supporters of Leicester City can look ahead to the coming season with a sense of optimism for the future and a belief in the direction Rodgers is taking them.
"There's a wave of optimism for the future," he continued. "Without doubt, there is a real air of positivity and expectation for the future.
"There’s a vision there. He [Rodgers] has a way of how see sees the Club moving forward under his tutelage and the players certainly look to be buying into that.
"He’s developing his approach, his style, already in the short time he’s been at the Club. There’s been an extra focus about the attacking side of Leicester’s game.
"Brendan speaks a lot about structure, but he’s added an extra dimension to the team with an attacking emphasis with the midfielders and full-backs also being pushed up further.
"He’s got a winner’s mentality, his track record proves that. The people who can be on his level at the Football Club will go with him on that journey, but he won’t be carrying people."