Kane opened the scoring inside the first 11 minutes before Ferjani Sassi struck later in the first half from the penalty spot to draw level in Volgograd.
While Kane took the plaudits, his manager was more interested in England's cool heads under pressure as they refused to deviate from their measured possession game that Southgate has tried to hone.
That BBC video is very much a tongue-in-cheek dig at the English reaction every time the World Cup rolls around and the responses to the video on Twitter suggested fans did not approve of the hype machine kicking into gear after so many false dawns down the years.
His two goals against Tunisia were his first at a major tournament after a goalless Euro 2016, but Kane's statistics for Tottenham (108 goals in 153 Premier League appearances) suggested that it wasn't going to be too long before breaking his duck on the biggest stage.
"He leads by example, he is a top forward and his career is only going to go up and up".
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Obama joined the conversation with a Monday afternoon tweet: "Sometimes truth transcends party", she wrote , and shared Mrs. Children are not detained with their parents when those parents are facing a criminal charge, as per US protocol.
"Poch sent me a text message with lots of love hearts emojis and he wrote: 'Come on, England!'" Kane said after the match.
England and Tunisia players swatted away swarms of gnats that flew into their eyes and mouths during their opening World Cup game in Russia's riverside city of Volgograd on Monday. "And may I remind you that I have 1 more Golden Boot than you".
"If we are creating that many chances - and who is to say we won't do that again? - we want to be as clinical as possible".
England will look to keep the momentum alive in its second match against Panama on Sunday.
It's a great start for England, but the evening didn't pass quite as smoothly as it could have for Gareth Southgate's men.
"The message we have is: we attack the tournament", added Kane.