The heated exchange between the Brazil international and the supporter was captured on video and occurred as Lionel Messi missed an injury-time penalty during Barca's 2-1 win in the last 16 first leg at the Etihad Stadium.
The fan celebrated Joe Hart's save from Messi's spot-kick in a provocative manner as the former Santos man sat on the substitutes bench, then mocked the Barca man by making a diving motion with his hand.
Neymar appeared to beckon the fan over before going to confront him at the final whistle.
Stewards intervened before Neymar turned his back on the supporter and headed down the tunnel.
"I was just playing with him," Neymar said. "He began to curse me and I ended up mocking him.
"What he told me? I can not repeat it, no. My mother gave me an education. What his mother did not tell him, my mother taught me."
