The Spitfires lost 2-0 to Barrow in the National League on Saturday, and were booed by their own fans after their seventh defeat of the season.
After the game, former Stevenage boss Hill told BBC Radio Solent: “They’ll (supporters) always point the finger at our performances and rightly so, but sometimes supporters have to look at their performance.
“I can pick a few games out this season where their performance wasn’t particularly good.”
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The comments got Hill into hot water with the supporters, and he has subsequently apologised.
“I don’t think in any way, shape or form that I blamed them for the defeat [on Saturday]," he said after Eastleigh's draw with Maidenhead on Tuesday.
“If they think I was blaming them for Saturday, I wholeheartedly apologise for that.
“It wasn’t meant that way. Sometimes I have a habit of saying what I think, whatever the consequences.
“What I’m prepared to do, if the fans want to, is donate £500 to a charity of their choice on the basis it’s gone and forgotten and we get on with things."
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