Kane normally takes the spot kicks for Spurs but missed yesterday's clash with Claude Puel's side due to an ankle ligament injury.
Dele Alli stepped up to take responsibility after being fouled by Steven Davis and promptly slotted home what proved to be a crucial goal against the Saints.
But the 20-year-old was not alone in voicing a desire to take aim from 12 yards and Pochettino was pleased to see several of his charges keen to take the ball too.
"For me it's OK. It's good that we have players who want to take the responsibility to shoot the penalty.
"Fantastic. With no Harry Kane everyone can take the penalty - no problem," Pochettino insisted.
Alli successfully sent goalkeeper Fraser Forster the wrong way to take his Premier League tally for the season to 14.
The midfielder was delighted to notch up another effort but admitted he had to make sure his teammates' could have nothing to complain about after taking the ball for himself.
"As soon as I realised H [Harry Kane] wasn’t on the pitch I saw it as an opportunity to get another goal so I grabbed the ball," Alli told Tottenham's official website.
"We didn’t really speak before the game about who might take it so it was first come, first served.
“When a few of the boys want it, you have to make sure you put it away. I was confident," he added.