Rice was handed an initial two-game suspension by the NFL for striking his wife in an Atlantic City hotel in February, which culminated in his arrest, although he was later placed in an intervention program.
However, last week CCTV footage was released of Rice's assault on his then-fiancee in the lift of the hotel, which demonstrated the violence involved in the attack.
Goodell came under immediate criticism for his light punishment of the 27-year-old and quickly altered his two-game suspension to an indefinite ban, while Rice was also released by the Baltimore Ravens.
Goodell said in a statement: "At our best, the NFL sets an example that makes a positive difference. Unfortunately, over the past several weeks, we have seen all too much of the NFL doing wrong. That starts with me. I said this before back on Aug. 28 and I say this now:
"I got it wrong in the handling of the Ray Rice matter, and I'm sorry for that. I got it wrong on a number of levels, from the process that I led to the decision that I reached.
"But now I will get it right and do whatever is necessary to accomplish that."
The NFL have launched an investigation into their handling of the Rice assault case, after a report from the AP claimed that they had the footage from the lift in their possession for three months.