Kuipers went to VAR early on in Tuesday's Champions League encounter, checking for an apparent handball in the box.
The review revealed that the ball had struck the outstretched arm of Danny Rose, prompting Kuipers to point to the spot, award a penalty and hand Rose a yellow card for the incident.
Clattenburg, who presided over a number of major matches including the 2016 Champions League final and the Euro 2016 final, says Kuipers made the right decision and used VAR correctly in the situation.
"In keeping with UEFA instruction, referee Bjorn Kuipers was right to award Manchester City a penalty when Danny Rose handled as he slid to block Raheem Sterling's shot," Clattenburg wrote for the Daily Mail.
"Rose's arm was outside his body and that, say UEFA, means the Spurs defender is making himself bigger. UEFA issued this instruction after similar incidents in the Champions League earlier in the season.
"It was always going to be a penalty once it was referred to VAR and Rose knew it, you could tell by the way his body slumped."
It proved no real matter, though, as Sergio Aguero went on to miss from the spot with Hugo Lloris making a diving save.
Clattenburg added that he feels some saw Manchester City's lack of protest as a reason to not go to VAR, but the former referee says Premier League players do not expect those penalties to be given due to the league's lack of VAR.
And Clattenburg, who added that "we don't want VAR to ruin the game with too many checks", says that Kuipers handled the incident well
"This is important, a referee should always make the final call," he said.
"If not, you spend the next five minutes worrying about whether the decision was right."
Spurs sealed a 1-0 win behind a Son Heung-min goal ahead of the second leg at the Etihad next Wednesday.