Leicester sacked Rodgers in April and appointed Dean Smith to save them from relegation.
But despite a win in the last game of the season against West Ham United, Leicester failed to hold on to their Premier League status after finishing in 18th place in the league table.
Kerr pointed out that Rodgers saw the need for a squad overhaul last summer, which Leicester failed to do during the transfer window.
The former Republic of Ireland boss also questioned whether the 50-year-old tactician overstayed at the King Power Stadium and believes that Rodgers foresaw that Leicester would go through a difficult season.
However, Kerr also stated that Leicester’s players were not consistent with their performances and did not do enough to keep them up in the Premier League.
When asked about whether Leicester going down is a surprise to him, Kerr said on Off The Ball: “Yes, it is remarkable really, but you wonder did Brendan Rodgers stay around too long?
“I would not say he saw the writing on the wall, but he saw in the summer that it’s going to be a tough season.
“I remember him saying last year that the team needed an overhaul and they did not really get that overhaul in the summer.
“It comes down ultimately to the players and they did not do it.
“They were not consistent enough and they conceded too many goals.”
Leicester finished the season in 18th place with a points tally of 34 and they will be hoping to bounce straight back up to the Premier League next season.
