Tierney won the Scottish Premiership and other titles with the Hoops in Scotland.
But when he decided on a move to the Gunners and the Premier League, some fans were not best pleased.
Speaking on the Open Goal podcast, Tierney said: "It was just sad the way it ended. People turning and all that.
"Some people make it out to be what it's not and it's not that at all.
"I'm like, 'this is breaking my heart reading this', and as soon as this gets announced it's going to blow up.
"And the worst thing I did when it got announced was go on Twitter. Thousands of tweets, threats and all sorts.
"When I went home, two days later after signing, there was spray paint on the walls, 'Judas' outside my bit."
Asked if he'd been back to Celtic, Tierney said: "No, I'm scared!"