McDermott, not one for attacking other clubs, took aim at Saints chairman Nico Cortese over the decision.
"I was favourite for the sack at the start of the season," he said, "but I've learnt. You learn from experience.
"If someone had said to me: 'This is how it's going to be,' I wouldn't have known because I hadn't been through it.
"What I find fascinating about owners is that managers who lose games start to learn. Then they pick up a few points, then they are sacked. Look at Nigel. (Adkins) He struggled at the start. Then he loses two games in 12 and gets the sack.
"Listen, it's their business but I'm talking about owners who sack managers who have come through it, it doesn't seem like the right thing to do.
"I just find it incredible.
"Let's have a bit of respect. That's not right. That's not right and proper. What he has done for that club has been phenomenal. Two promotions...they are finding their way in the Premier League.
"I've texted Nigel and he texted me straight back. He's a great guy and a fantastic manager.
"He's done a great job at both Scunthorpe and Southampton. I'm sure he won't be out of it for long."