BBC boss Tim Davie said he regrets that audiences were affected when Gary Lineker was briefly suspended from the corporation but said the presenter's Twitter activity "hasn't been a concern" of his since.
Lineker was taken off air by the broadcaster after posting a tweet in which he said the language used by the UK Government to promote its asylum plans was not dissimilar to 1930s Germany.
The 62-year-old shared a video of Home Secretary Suella Braverman announcing details of her new Illegal Migration Bill and commented in March: "Good heavens, this is beyond awful".
Lineker said in a later post on Twitter: "This is just an immeasurably cruel policy directed at the most vulnerable people in language that is not dissimilar to that used by Germany in the 1930s."
However, the £1.35 million a year BBC star was criticised by various public figures across the political spectrum for the post.
BBC director general Tim Davie (Photo: Parliament TV)
Speaking in March, Mrs Braverman said she was "disappointed" by the comments, while her opposition counterpart Yvette Cooper told LBC that he was "wrong to say that".
He returned to Match Of The Day after a boycott by top on-air talent and the BBC launched an independent review of its social media guidance.
Asked by MPs if he regrets how he handled the situation with the Match Of The Day host earlier this year, the BBC director-general told the House of Commons Culture, Media and Sport Committee: "It was certainly a busy weekend. I regret audiences were impacted at the end of the day.
“The idea that we didn't put out a full programme I'll always regret."
Asked if he is happy with how Lineker has tweeted since Davie added: "That hasn't been a concern of mine.
"What's been a concern is getting the social media review to a point where it can be delivered flawlessly, and that is not easy."
He added that he is expecting that report back to them "pretty soon".
Davie went on to say that it had been "tough" deciding where to draw the line between social issues and party political issues while conducting a social media review for employees at the corporation.
He added: "We are obviously doing the social media review... It's been tough in terms of where do you draw the line between social issues and party political issues, tone. I think we want to find the right balance."
Dave also said it was "not right" to say that everyone across the BBC did not have a right to express a view.
"And I think audiences are smart, they can say, 'Okay this individual has views but they're presenting a nature programme'."
