Nosworthy flashed a raised finger as Blades' players headed towards the tunnel at half-time during the 4-2 defeat at Turf Moor.
The defender, who is on loan from Sunderland until the end of the season, had been singled out for jeering over his part in two of Burnley's goals.
He was substituted by new manager Micky Adams at the break but had suffered an ankle injury and misses today's South Yorkshire derby against Doncaster Rovers at Bramall Lane.
News of his substitution sparked cheers from Blades supporters and, speaking after the game, Nosworthy was full of remorse.
"I am sorry for reacting to whatever was said because I know I am bigger and better than that. It won't happen again," he said.
"I know the fans are disappointed with what's happened but I take full responsibility. They pay their money to come and watch us perform. It was frustration on my part and I lost my rag.
"It was an individual who I reacted to," he said. "To hear things from your own fans is frustrating but I've been there and done that. I usually just take it on the chin and get on with it.
"It was poor by my standards and I say sorry to all the fans if they felt that it showed I don't care – that's the last thing I feel. I care a lot, and I play with my heart all the time.
"There is still a job to do and I very much want to be a part of that to help the team get out of the situation we are in," he stressed.
The Blades are only two points above the Championship relegation zone after suffering five defeats in their last six games.
Nosworthy had been playing with a sore ankle for three games and a first-half challenge from Burnley striker Chris Iwelumo at Turf Moor made the problem worse.
"I hold my hands up. It was a lack of concentration for the second goal," he said.
"I feel I am to blame for that goal but, obviously, I am carrying an injury as well.
"I don't like losing and I am now injured so there's double frustration."
New manager Adams had to make do without four banned players and five players with long-term injuries for his first game in charge of the club.
Although midfielder Nick Montgomery and defender Kyle Bartley will return from suspension today, there are fresh injury concerns over another five players.
"It never rains but it pours," said Adams, who is looking to the loan market in an attempt to bolster his options.
"We have a few more problems injury wise but we have to come out fighting against Doncaster at Bramall Lane."
Defenders Jean Calve and Matt Lowton and midfielder Leon Britton all suffered groin strains in the game at Turf Moor.
Former England goalkeeper Richard Wright started only his second game for the club but, as in his first at Barnsley last month, was unable to finish due to a thigh injury.
Midfielder Lee Williamson lasted 72 minutes on his first appearance since a back operation in the summer but was substituted on medical advice.
Adams will check on Williamson's fitness this morning before deciding whether he should play against Rovers.