Hill questioned why his team were booed off at full-time on Saturday by the Eastleigh fans following their 2-0 home defeat to Barrow.
The Spitfires came back from two down to draw last night against Maidenhead United and Hill offered to make amends for his comments afterwards.
He told BBC Radio Solent: “I was critical of the fans Saturday. I don’t think in any way, shape or form that I blamed them for the defeat.
“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.
“Tonight, they got behind us great from the start and at the end they’ve clapped the players off and it’s been a long time since that’s happened at home.”
For more coverage, reaction and some of the best moments from games going throughout the season, head to our social media channels on Twitter, Facebook and now Instagram.