The text mistakenly popped up on the news ticker at the bottom of the screen during a tennis update just after 0930 on Tuesday.
She said the mistake had occurred as someone was learning how to operate the ticker and was “writing random things”.
Another message which appeared on the ticker read simply: “Weather rain everywhere.”
Mcveigh told viewers: “A little earlier, some of you may have noticed something pretty unusual on the ticker that runs along the bottom of the screen with news making a comment about Manchester United, and I hope that Manchester United fans weren’t offended by it.
“Let me just explain what was happening: behind the scenes, someone was training to learn how to use the ticker and to put text on the ticker, so they were just writing random things not in earnest and that comment appeared.
“So apologies if you saw that and you were offended and you’re a fan of Manchester United.
“But certainly that was a mistake and it wasn’t meant to appear on the screen. So that was what happened, we just thought we’d better explain that to you.”
An official BBC statement added: “There was a technical glitch during training with our test ticker, which rolled over to live programming for a few seconds.
“We apologised for any offence caused on air.”
BBC presenter and Manchester City fan Clive Myrie tweeted he “had nothing to do with this!!” with the hashtag MCFC, after City won the Premier League title on Sunday.
Manchester United have struggled by their standards in recent seasons and missed out on a Champions League spot, coming sixth in the table. Their new manager and former Ajax boss, Erik Ten Hag, is United’s fifth permanent boss since Sir Alex Ferguson retired in 2013.
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