Manchester United lost 1-0 to Everton in the Premier League at Goodison Park to put a dent on their Champions League prospects.
The Red Devils now find themselves in seventh position, six points behind Tottenham Hotspurs, who occupy the final Champions League spot.
After Anthony Gordon's first half goal gave Frank Lampard's side the win, Ronaldo took out his frustrations on a young Everton fan on his way into the tunnel when he smashed his phone.
The moment was captured on video and made the rounds on social media afterwards.
Ronaldo, who endured a frustrating afternoon, has come out to apologise for his behaviour and has invited the Everton fan to a future Manchester United home game.
"It's never easy to deal with emotions in difficult moments such as the one we are facing," Ronaldo wrote.
"Nevertheless, we always have to be respectful, patient and set the example for all the youngsters who love the beautiful game.
"I would like to apologise for my outburst and, if possible, I would like to invite this supporter to watch a game at Old Trafford as a sign of fair play and sportsmanship."
Ronaldo has scored 18 goals this season but has not found the back of the net in any of Manchester United's last three games.
