Kane meanwhile said he would like to wear the armband in the long term, but that the manager had given no indication on a permanent decision.
Southgate said: "People have said to me there were a lack of leaders in the team and I don't see that to be the case".
"But everyone stood up to it". They dug deep and found a goal out of nothing really, so that's what it's about.
"Whatever anybody thinks about us as a group of players, one thing you can't question is their personality, character and commitment". We have got leaders in the team, and it is just that I am wearing the armband.
"It is fundamental to being a top team but it is only one step in that direction, we can still improve in all areas, we all know that, but nevertheless it is a significant moment I think", he said. To score that goal, it was a special feeling for me'.
"Our objective is to qualify and we're still top of the group". Before the game we would have taken the point but it was just the way it happened, but that's football for you. "Butland was in pole position before he got that injury in Germany previous year".
"I don't think it was tougher than what we expected because we always expect to have tough games, especially against your rivals". It will be a good game, a good test against one of the best in the world.
"It's a game we should win, a game we were in total control of", the England boss told ITV.
Scotland hero Griffiths was left "gutted" despite scoring a brace of free-kicks for his first goals in the dark blue.
England were heading for a first qualifying defeat since October 2009 after Leigh Griffiths struck two glorious late free-kicks to wipe out substitute Alex Oxlade-Chamberlain's 70th-minute opener.
England captain Harry Kane relished an "incredible" atmosphere at Hampden Park as his side snatched a late point with a 2-2 draw against Scotland.
Kane was in again five minutes later with the best chance of the first half, but missed Adam Lallana's cross completely, albeit a ball that was slightly behind him.
"Today we've done that".
The Celtic man added: "I am delighted to get off the mark for Scotland, in what could have been a great win, but in the end this could be a great point for us". I still talk, I still shout in the same way. I will look at the players and tell them you have to keep coming back and taking knocks like that. Seriously, for decades that will haunt us. But three goals in the final six minutes lit up a game that was until then low on quality and entertainment.
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