The 21-year-old moved to Stamford Bridge for £70million after a protracted transfer which saw him fail to show up for training with the Foxes.
A message appeared on Fofana's Instagram account on Wednesday accusing Leicester of making "false and misleading comments" amid the saga while also aiming a dig at Rodgers, saying he "exposed" the defender.
But Leicester boss Rodgers does not believe his former centre-back is to blame.
He said: "I would say the post didn't come from Wesley. I know that for sure because of my experiences where I had a message from Wesley.
"The post is a cheap shot towards the end from people, rather than him. The kid is a great lad. I'm not happy he has left because I've lost a top player.
"I'm not going to sit here and destroy a young lad when I know really where the message has come from. We're sad he has gone, we wish him all the best and we'll move on.
"I never get too emotional with words. Wesley was exposed to a club when very few people knew who he was. We brought him here as a 19-year-old, put him in the team, his profile went worldwide and he was absolutely brilliant.
"He got injured, the club could have been exposed but they weren't, looked after him, gave him a new contract and his agent would have done really well as well.
"We felt he was going to be here. I felt he wanted to be here. But the game changes."
Leicester go to Brighton on Sunday after Thursday's 1-0 defeat at Manchester United left them winless and bottom of the Premier League.
Ricardo Pereira (Achilles), Ryan Bertrand (knee) and Daniel Amartey are out but Wout Faes could make his debut after joining from Reims.
Faes was the only outfield player signed this summer, replacing Fofana, with Rodgers admitting he was frustrated the club had cut back on spending.
Chairman Aiyawatt Srivaddhanaprabha wrote in Thursday's programme that FFP and Covid were two of the biggest reasons for the Foxes' position.
"I'm in the know within the club and frustrated for the supporters outside who aren't," said Rodgers.
"They see all the other teams getting lots of players in and we're not getting any so there's that little sense of frustration.
"But I can only look at the team and what I can control. For the first game here against Brentford we were excellent for an hour and we should have won the game but ended up drawing.
"Against Southampton we played really well, it's 1-0 and we somehow found a way to lose. At Arsenal we were beaten by the better team.
"Chelsea we should have got something from and then against Manchester United I thought we deserved something.
"It's not as though the players are downing tools. We're giving everything but we're making some mistakes and lacking quality in certain areas."