The in-form 20-year-old made it six goals in four appearances for the Young Lions in Milton Keynes, hitting a brace that complemented Michael Keane's early header in a 3-0 win.
Berahino celebrated his first goal in the Euro 2015 qualifier by paying tribute to his father, who was one of the estimated 300,000 killed in the civil war that plagued Burundi.
The striker was booked for showing a shirt with 'RIP Love U Dad' scrawled on it - something he apologised to Southgate for at half-time.
"He is a good player, a good finisher and a pleasure to work with," the Under-21s boss said.
"He has got a desire to improve all the time and he is a terrific goal threat for us.
"That said, looking at our bench tonight we have some super players I didn't put in the starting line-up that I think can cause a lot of problems.
"I hadn't realised he had been booked until he came and apologised at half-time. I couldn't quite work out what he was apologising for.
"The rules are what they are and again that is something we've got to learn. Hopefully it won't be too costly for us.
"I think it was a personal thing that he had done it for, but had I have known I would not have let him go out there with that on his shirt."
- Sports & Recreation
- Michael Keane