The midfielder was involved in an incident with the Portugal international after Wednesday's game, and has now conceded that he may have insulted his opponent
The duo had an exchange of words after Los Blancos recorded a 3-0 win over the Basque side to secure their 32nd Liga title, before the Portugal international made an insulting gesture toward his opponent.
"Something happened after the game, but things like this happen all the time. Basically I told him to stop pointing at the stands. I might have called him a 'son of a b****', but players refer to my mother every game and nothing ever happens," Martinez explained to Onda Cero.
"People should not think too much of the incident. Sometimes you're a bit hot-headed and you say things you later regret. We will just shake hands when we meet again next year, and nothing will come of it."
Cristiano Ronaldo has yet to comment on the incident.
Since March, Goal.com has been publishing exclusive extracts from Luca Caioli's new book, Ronaldo: The Obsession for Perfection. This Friday's excerpt looks at the mutual appreciation between Cristiano and Jose Mourinho after the two Portuguese led Real Madrid to La Liga glory earlier this week. Don't miss it!