Kosovo took the lead after 35 seconds following a mistake by defender Michael Keane and, although England responded with five goals in the first-half, they endured a nervy finish to the game after conceding twice in the second-half.
Goals from Raheem Sterling, Harry Kane and a brace for Jadon Sancho highlighted England’s attacking might but Southgate was less than pleased with his backline.
“It was bizarre. The outstanding features and poor features are apparent to everybody,” Southgate told reporters.
“Poor individual mistakes, a poor start. I like the way we showed the composure to recover from that initial mistake and our use of the ball throughout the first-half was excellent.
“The small period after half-time: ridiculous mistakes, poor decisions, lack of covering back. We made the game uncomfortable for ourselves. There were mistakes that were concerning ... they were such basic errors ... that you have to learn from.”
England lead Group ‘A’ with 12 points and can qualify for the finals of the tournament with a win away to the Czech Republic in their next game on October 11.
Separately, FA technical director Les Reed said it would be difficult to retain Southgate’s services if the former England international decides to manage in the Premier League.
Southgate guided England to the semi-finals of the World Cup in Russia last year and third place in the Nations League in June, making him a sough-after coach.
“It would be a tough ask depending on what he was offered,” Reed told Sky Sports.
“It’s something that we have in the back of our minds all the time but I know that Gareth’s motivation is with this team and developing this team moving forward ... he wants to be an England manager that wins something,” he said.