Ten Hag had a dig at Keane's managerial record after the Irishman's constant sniping at him this season.
Keane said to him: "You must be proud of them, we've always questioned players about their quality at Man United, but character and leadership.
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"They showed character today - which I had questioned, and a lot of people have...you shouldn't listen to them pundits anyway! Take no notice of the pundits."
Ten Hag said in response: "But you told me!"
Ten Hag then told Keane: "You had trouble to manage a team!"
Keane replied: "Ah, I won a Championship with Sunderland...give me some praise, ah come on! You're too harsh on me!
Ten Hag tried to explain "what I said to you" before Keane jumped in to say "I agree" as both men were able to share a laugh.