Bristow had posted on Twitter that darts players were "tough guys" and footballers "wimps".
In a heated interview with host Piers Morgan on ITV's Good Morning Britain, Bristow initially defended his tweets, saying he was trying to encourage children to report abuse immediately.
He later accepted he had offended people and said: "I am sorry for that."
Bristow added: "I apologise, it was mis-worded. They are not wimps."
In a statement issued later on Wednesday, Bristow described himself as a "bull in a China shop" and said he now "appreciated my wording was wrong and offended many people".
"It makes me furious to think that an abuser can get away with it for so long, and to so many, when they should always be looking over their shoulder in fear, waiting to be confronted," he said.
"I know why I've been vilified but if one child comes forward quicker or one abuser thinks twice about the likelihood of being confronted then it will have been worth it."
The 59-year-old was dropped by Sky Sports on Tuesday after asking why victims did not "sort out" their abusers "when they got older and fitter".
Newcastle United said they had dropped Bristow "immediately" from a scheduled appearance at St James' Park on 6 December and "will not work with Eric Bristow in the future".
His manager asked for a £5,000 fee for Bristow to appear on the BBC to discuss his comments. GMB said it didn't disclose guest contracts - and Bristow later said any money received would be donated to charity.
Nine police forces are now investigating allegations of historical sexual abuse, with more than 20 former footballers having made allegations to the Professional Footballers Association and a special NSPCC hotline receiving more than 100 calls.
The Football Association has instructed independent leading counsel Kate Gallafent QC to oversee an internal review of what it knew and when.
On Wednesday, the BBC's Victoria Derbyshire programme reported that the FA scrapped a major review of its child protection policies in 2003.
Ex-darts world champion Eric Bristow has apologised for suggesting football sex abuse victims are not "proper men".