The Manchester United striker appeared to slap the young supporter's hand as he left the pitch moments after his side were beaten 1-0 at Goodison Park on Saturday, 9 April.
Merseyside Police say the football star was interviewed earlier in August in relation to the alleged assault and criminal damage.
A force spokesperson said: "The matter has been dealt with by way of conditional caution. The matter has now concluded.”
After footage of the incident went viral online, the Portuguese player publicly apologised to the 14-year-old before inviting him to Old Trafford.
The father-of-five blamed the emotional "outburst" on his club's 1-0 defeat.
In an Instagram post at the time, he said: “It’s never easy to deal with emotions in difficult moments such as the one we are facing.
“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.”
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