Pochettino's job is already in danger according to reports just three months into a five-year deal after Tottenham crashed to a 2-1 Premier League defeat at home to Stoke City last week.
Tottenham have lost three of their past four league fixtures to languish in 12th position after 11 rounds.
The North London team's current plight has led to speculation that chairman Daniel Levy could part ways with the Argentine boss.
But Klinsmann - now in charge of United States' national team - has called on Tottenham to be patient as Pochettino attempts to rebuild the squad.
"I wish Mauricio only the best. I think he's a tremendously talented coach," said Klinsmann, who spent the 1994-95 season at White Hart Lane. "He's shown that already. He's got a smart brain. We'll see over time how things work out.
"You always want to have the crowd on your side. That comes from what happens on the field. If a game doesn't go well then the crowd has every right to be a bit pessimistic.
"I actually thought the crowd tried to give positive energy to give them a push. A goal was pulled back to make it 2-1 came and I had the feeling that the equaliser would follow. But it wasn't to be.
"Every coach needs time to put his mark on an environment, on a club, on a national team programme. Wherever you work, success will only happen over time."
Klinsmann added: "Unfortunately, professional football is driven by short-term results, high media expectations and high fan expectations and that often drives clubs to make very quick decisions just because they have lost five games in a row.
"If you want to evaluate the work of a coach then you can only do that over a longer period of time. That's the way it is. In every other working environment you need and get that.
"In order for Mauricio to put his stamp on Spurs he needs a couple of transfer windows to build the team he has in mind, to put the puzzle together that he envisions."
