England led after just 12 minutes against Serbia through Jude Bellingham’s bullet header, and controlled the first half in Gelsenkirchen.
However, they only had five shots in the match as Serbia controlled possession after the break, and Southgate admitted England would have to improve against the side they faced in the Euro 2020 semi-finals.
“We know we have good players, we know we can play better than the other day,” he said.
“But I thought the players, in an incredibly pressurised moment, started exceptionally well and defended brilliantly throughout the whole game. I think they’ll be better for having a game under their belt.
“Emotionally there’s so much tension, I don’t think people can really understand what it is like for young players. We are pleased to have got a result from that and we know we have to be good tomorrow.”
One player who will not face Denmark is defender Luke Shaw, with Southgate confirming the Manchester United left back has not recovered from his hamstring injury in time.
“Luke won’t be involved tomorrow, he’s on track for what we thought originally,” Southgate said.
“He needs a bit more work. There are days when he needs to do more than the rest and needs to recover.
“He’s still in and out with the others and operating on his own programme as well.”