"There's no question that towards the end of our time here Steve and myself didn't get on so well," Southgate told the Sunday Sun.
"But I still respect the job that he did here and having become the manager, you obviously see a lot of the difficulties that he faced, so you have a greater understanding of it.
"The fact remains that as manager and captain we had a very successful period here, so it was good to hear his support.
"It's been good to see Steve do well in Holland with FC Twente, they've had an excellent season. He proved with us that he's a good manager. Unfortunately for him the circumstances with the England job meant he felt he needed to go abroad.
"But I'm sure that experience will stand him in good stead, and he'll be better prepared for the next opportunity that comes up in England."