Ole Gunnar Solskjaer went in to the match looking to maintain his ideal record having won all five of his matches in all competitions since replacing Jose Mourinho as United manager last month.
Spurs were unable to make the most of their second-half superiority at Wembley and succumbed to Marcus Rashford's first-half strike, with Kane among the players to be kept at bay by an inspired David de Gea in the United net.
"We won the game against a top team, we controlled the first half but in the second half they had chances", De Gea said. "That's where we improve, progress and get more experience".
However senior FA insiders refused to be drawn into any sense of panic on Sunday, and sources close to Southgate, 48, said they could not see him walking out on the national team after reaching last year's World Cup semi-final, and given the prospect of a 2020 European Championship that could see England play most of their games at Wembley.
"I am enjoying playing football".More news: No-deal Brexit would be 'disastrous', says United Kingdom minister
If it wasn't already abundantly clear, Pogba is far happier playing under Solskjaer than he was Mourinho. "It was really hard playing in the system we used to play". Defending is not my best attribute.
"It was a big one for us". We needed to attack on the opposite side, that's what we did and we scored a goal.
United were a particular danger on the counter and it was no surprise to see them ultimately go ahead at the end of such of a move, with Rashford finishing after Paul Pogba's excellent pass.
After talk in the build-up to the game that the match was an opportunity for Pochettino - linked to the United job - to take on interim Old Trafford boss Solskjaer, the Tottenham manager was asked how he felt he fared.
"He makes a great run, he helped me for the pass, I tried to give him the ideal pass".