Moyes' men travel to St Mary's on Monday in what will be Mauricio Pochettino's first game in charge of the Saints.
The Argentinian was immediately installed after Adkins was shown the door, despite the manager having taken Southampton to successive promotions and 15th in the Premier League table.
Moyes said: "I'm very surprised. I was talking to my staff during the week and complimenting how well Nigel Adkins had done. It was always going to be difficult after two promotions. Anybody who does that coming up, it's a long way up.
"He'd just got himself out of the bottom three and moved up and I don't think there would have been many people looking at Nigel Adkins to be sacked in that position."
Moyes celebrates 11 years in charge at Goodison Park this year and he said the trust shown in him by chairman Bill Kenwright and the board is an increasingly rare commodity in football.
"I don't know if we are scratching our heads any more, and that's probably the football world we're in. I'm not saying it's the right one, and I'm not just willing to brush it aside. But that's the way it looks just now," he said.
"I'm really fortunate and, if you look at the clubs who have kept their managers for longer periods, I think that's tended to work better than continually changing managers."
Southampton v Everton is live on Sky Sports 1 this Monday. For more details click here http://www1.skysports.com/footballonskysports/8395413?DCMP=FootballHub_SouEve_Editorial