The Gunners suffered a shock 3-0 defeat to Brighton on Sunday to all but end their title ambitions in the Premier League.
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And Keown was not over it, reacting furiously on talkSPORT on the White and Jordan Show, taking issue with Sky Sports and Martin Tyler.
It led to a huge reaction on social media, with fans responding on both sides of the argument before former Leeds defender Mills chimed in.
The former Leeds and Man City defender texted host Jim White to take aim at Keown in a savage blow to the Gunners legend.
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"This is from Danny Mills, walking the dog: 'Same old Arsenal. They flapped at it in 2002 and 2003.
"'They lost at home to us [Leeds United], Martin on that day was bullied by Harry Kewell, Alan Smith and Mark Viduka.
"'As for Martin Tyler, he loves Thierry Henry and he loves Robert Pires. Martin is showing signs this morning of paranoia, insecurity and is being a bit pathetic'."
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Given the floor to respond, Keown sarcastically replied: "Oh Danny Mills, yeah. One of England's finest-ever full-backs. Danny Mills."
An awkward silence fell for a second before White intervened and said: "Okay Danny Mills, walk the dog and if you feel like it, ring in and give us a call!"
Keown had caused a stir with his comments as he, along with the other Gooners, watched the title dream slip away.
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He was part of the last side to be crowned champions in 2004 and it was tough to take.
Arsenal have just two games remaining and need City to lose their next three matches.
Should they beat Chelsea on Sunday, they will be crowned winners.