St Johnstone manager Wright gave Lowe an earful after feeling referee Don Robertson’s red card for Mackay was “a really poor decision”.
It came at the start of the second half of a drab game against Caley Thistle, which the Saints nicked with a late Liam Craig penalty.
The visiting boss admits giving the fourth official stick but has since made amends after reviewing the incident.
He said: “Having seen it back, I went in and apologised to him. I can see why the ref has given it but I think with the pace that Dave has gone in, maybe on another day the ref could have given him a yellow. I don’t think we can appeal it because there isn’t enough in there to give us a case.
“I don’t think there was any real intent in it but his foot was slightly high, even though he did get some of the ball. Maybe the reaction of the player as well influences the referee but I can see why he gave it.
“I still think it could have been a yellow but I did apologise because initially I thought it was a really poor decision, but as it turns out it wasn’t.”
His counterpart John Hughes is hoping for a reaction from his side for the League Cup quarter-final clash with their neighbours Ross County tomorrow night.
Caley Thistle were poor on Saturday and failed to take advantage of Mackay’s dismissal. Although the red card opened the game up somewhat for the home side, with James Vincent and Miles Storey able to stretch the Saints defence, the closest they came to scoring was a Liam Polworth effort that strayed wide 15 minutes into the second half
Referring to the looming Highland derby, Hughes said: “There’s no better game for them and they’ll raise themselves. I hope they go away angry because I’m a great believer that you have to play on emotion. Hopefully what happened today gets them geed up for Tuesday. It’ll be a great game, great for the Highlands and I’m really looking forward to it.”