Everton will be new manager Mauricio Pochettino's first opponents in Monday's league game at St Mary's.
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."