Jude Bellingham struck for the opening 1-0 triumph.
Southgate later said: "They are a strong team. We had to suffer a bit which I think is really good for us. I think to defend the box the way we did was really good for us. I was really pleased with a lot of the play. Second half we didn't keep it as well as I would have liked but to get the win is very important."
On Bellingham, he continued: "He writes his own script. The timing of his runs. It was a super bit of play in the build-up of his play. I think all of our forward players looked really good.
"I am confident we will score goals. Playing against a back give it is not easy to create chances and we did. I liked the fact we had to suffer without the ball because that is an area we have worked on a lot this week. We were obviously much better than last week at doing that."
Trent Alexander-Arnold played in midfield and Southgate added: "I have to say, he has been really diligent in getting his positioning right. I think he adapted and adjusted really well and used the ball well. We have got a squad and we need to use it."