In the tweet, which was later deleted as the FA issued an apology, United's Chris Smalling was asked "what's in your pocket?" along with a short video of the defender saying "Harry Kane".
Kane has been the centre of attention, mocked my rivals for successfully appealing Tottenham's second goal against Stoke City earlier this month after it was initially awarded to team-mate Christian Eriksen.
Spurs attacker Alli, meanwhile, has also been booed for diving throughout the season, and Pochettino said the pair should be backed heading into the Russia 2018 showpiece.
"[The criticism] is a little bit strange from my point of view. Both Harry and Dele are massive talents and they are going to defend the England national team shirt," Pochettino said.
"But I think the people love Harry Kane and Dele Alli. It is in fashion sometimes to boo or criticise [players] like this but I think people love them but it is true sometimes we magnify the situation and we create an issue when really there is not an issue.
"But yes, sometimes [the criticism] is difficult to understand. Like it was so difficult to understand this tweet from the FA after the game of course."
Pochettino added: "For me, the most important thing here in England is try to back English players. It is so important for English football to back them. Kane is going to compete in international games at the World Cup and everyone wants to support the national team.
"If Harry Kane scores he is an English player not a Tottenham player or United or Chelsea, something like that.
"The most important thing is to back them. I don't think people need to show more respect -- it is only to show a little bit more love to them because, sure, this type of situation, like the one that happened after the game [against Man United], doesn't help to create a good atmosphere.
"And I'm sure that Harry is not happy and no-one is helping him to have an unbelievable World Cup. When we talk about passion, when we talk about to feel you are proud to defend your country and everything we need to be careful in the way we send messages or the way we write or give our opinion."