Davis, however, insists he retains a good relationship with the Gers support.
"Some fans were understanding but I got some abuse from others. You get hate mail and different things have been said, which isn't nice.
"But that's a minority and I certainly don't focus on that or let it affect the way I think about Rangers and the fans.
"The fans think the players are jumping ship, but I was actually glad Rangers eventually got a fee for me. I've got a lot of respect for the chairman at Southampton for agreeing to pay a fee in the end, so at least Rangers got something.
"I'm delighted to be at Southampton now and I'm looking forward to the next chapter of my career.
"Today's game against Manchester United is just the sort of game I joined the club for.
"Southampton have had a lot of success over the last couple of years and both the chairman and manager have got a lot of ambition.
"We're under no illusions it will be a big challenge in the Premier League, but it's one we are all up for."