Martinez, known as Licha to team-mates and fans, was moved after hearing United fans singing for him, following the full-time whistle, on the back of another solid display at the heart of the defence.
Our centre-back headed towards the tunnel and was welcomed by chants of 'Argentina, Argentina' - his homeland.
"To be honest, it's very emotional for me [hearing the fans sing for him]," he told club media in a post-match interview.
"I'm at one of the best clubs in the world," he enthused.
"This stadium, the atmosphere is amazing. When I heard the fans singing, I wanted to cry.