An eventual game at Brisbane Road saw the Spitfires and the O's share the points in a 1-1 draw in the Vanarama National League.
Comments came out after the game suggesting that Hill, who returned for a second spell in charge last March, has been disparaging about the East London club.
Hill was quoted as saying "them celebrating a draw with Eastleigh shows what has happened".
But the manager says his comments were taken out of context.
Hill said: "At no point would I ever be disrespectful towards another club in that way. The reaction has led me to believe Leyton Orient fans feel I have been, and I would like to clarify this.
"The comments were more a positive toward Eastleigh Football Club and what we have achieved.
"I did not mean, like it has new taken by some, as 'look what Leyton Orient have been reduced to' - not at all.
"It feels like I have been made a scapegoat for the problems - I am not the sort of person who would publicly have a go at another one and I feel I need to set the record straight."
Hill, whose team face Aldershot Town at the Silverlake Stadium tomorrow, added: "If people listen back to my pre-match comments about Leyton Orient you will hear me saying very positive things about the club.
"Of course we were gutted to not take three points on Saturday. Orient scored in the 7th minute of injury time and we felt we had done enough to win the game but that's football.
"But, as I said at the time, when you a so close to winning at a place like that it shows how far you have come."