England, who were not impressive overall, remain top of Group F on 14 points while Scotland are in fourth spot on eight points.
And the former Celtic boss was clearly frustrated as he flung a bottle during an X-rated tantrum. It's special. It could be a big point for us.
"We are disappointed but we have got to be proud of ourselves".
Scotland then finish the qualification campaign at home to Slovakia and away to Slovenia.
"Obviously we wanted to win the game, there is no doubt about that, but we got a point, are still top of the (qualifying) league".
Kane's goal was the Tottenham Hotspur striker's sixth in 18 worldwide appearances and came at the end of his first game under Southgate, after injuries had kept him out of England's six previous matches.
"You have to expect the unexpected and we were 2-1 down from nowhere but we found another gear". We know how good this England side are.
The 23-year-old said: "It looked like we're going to win the game and all of a sudden, it looks like we're going to lose".
Scotland's deep-lying 5-4-1 system starved England's creative players of space, but gradually cracks began to appear. I've shared the leadership around and that has been important for us as a team. You can't do any more than they did.
Southgate, who reserved judgement on Joe Hart's attempts to save the free-kicks, said: "We deserved to be ahead and then there was a mad minute and a half".
Strachan added: "I saw Scotland's best ever free kick and then I see Scotland's second-best free kick, and then I have a noise that I have never heard anything like before".
"Whatever anybody thinks about us as a group of players, one thing you can't question is their personality, character and commitment. It's about getting the most out of the players you've got and he does that".