The social media network says “being the target of online abuse is not easy to deal with” on a dedicated help centre page about coping and reporting abuse.
Yet on Tuesday it engaged in such behaviour when taking aim at the centre-back, with its verified @TwitterUK account posting: “Name a better footballer than Phil Jones”.
United are understood to have complained to Twitter about the subsequently deleted post, with the social network apologising to both club and player.
England international Jones has endured a tough season and missed out on the Europa League finals squad with an ankle injury.
He last featured for Ole Gunnar Solskjaer’s team in January’s FA Cup fourth round win at Tranmere, netting the fourth goal in a 6-0 romp.
A Twitter spokesperson said: “Our aim was to showcase our new product feature, conversation controls, which allows you to select who can reply to a Tweet.
“It was not our intention to cause upset and once we realised our mistake, we immediately deleted the Tweet.”