Nigel Adkins led Saints to back-to-back promotions and Wednesday's fightback to draw with Chelsea left them in 15th place in the Barclays Premier League table, three points clear of the relegation zone.
That was not good enough for the owners of Southampton, though, and on Friday Adkins was sacked and replaced by Argentinian Mauricio Pochettino, formerly manager of Espanyol.
Everton will be Pochettino's first opponents in Monday's league game at St Mary's, and 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 will celebrate 11 years in charge at Goodison Park in March but the faith shown in him by chairman Bill Kenwright and the board is an increasingly rare commodity in football.
Some Everton fans have grown increasingly impatient with Kenwright's failure to secure more financial investment, but Moyes is in no doubt what he brings to the club.
The Scot said: "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.
"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. I do think I'm really fortunate because of the board I work for and the chairman I work for. At times they've had to show patience with me but I hope in the end people will look at it and say it's the right thing to do."