Tim Cahill and Aleksandar Kolarov appeared to exchange words while Phil Neville was involved in heated discussion with Mancini and his assistant Brian Kidd.
When asked what sparked the incident, Mancini said: "I don't know because I wanted to take off Kolarov. I don't know what upset them."
Moyes said: "It wasn't Phil Neville. I think one of their players said Seamus Coleman had elbowed them or something like that, but it was nothing.
"All the fighting was done in the 90 minutes, not after the game."