England were expected to comfortably beat their northern neighbours but the final whistle was greeted by some boos from among the 20,000 supporters at the national stadium.
“Look, it’s a game we know we didn’t hit the level we wanted to or need to, but tonight we have to accept whatever comes our way,” Southgate said.
“All I would say is I’m totally understanding that as the manager, I totally understand anything that comes my way.
“What we need to do is make sure we get behind the players because there’s a lot of young players that need the support of everybody.
“Most of them haven’t been involved in a game like that before and they are unique occasions.
“They’ll learn a lot, they’ll bounce back from it but they need everybody behind them.”
Asked if he was angry with fans for booing at the end, Southgate said: “I think our fans are entitled to react however they want.
“We’re disappointed with our own performance and I totally understand their reaction.
“We were expected to beat Scotland. They’ll be frustrated by that and in the end we’ve got to live with that and deal with that.”
Steve Clarke pleased with Scotland’s performance against England
Southgate admitted he was reluctant to throw caution to the wind in a stretched second half by introducing more of England’s array of attacking players from the bench, and said it was important they considered the context of the tournament rather than the night at Wembley.
“I would say we had a fourth attacking player in Mount throughout the whole game,” he said. “I think in those moments, if we had to chase to win with no consequence for conceding you might approach it differently but it was a night where it was a bit frantic, there was not a huge amount of control and sitting on three points as we did, we manage the points as well as the game. It’s easy to gamble towards the end, lose the game and you’re kicking yourself for not managing the tournament.”
For the second game running, England captain Harry Kane was replaced by Marcus Rashford after a subdued performance in which he again failed to register a shot on target.
Southgate insisted the whole team needed to improve and praised Scotland’s back five for denying Kane the space to thrive.
“I think the whole team have got to look at the whole performance and our use of the ball and review where we can be better,” he said.
“That’s right across the board. It’s not about one person. Scotland marked him extremely well, with the back five there’s not a lot of space. Tonight we couldn’t find the answers but we go away to review the game and find those answers for the Czech Republic.”