Stewards handed Perez a drive-through penalty for an incident on lap eight of Sunday's race. Fighting for position with Romain Grosjean, he moved up the inside of the Lotus driver on the run to Les Combes.
However, Perez's move to take the racing line squeezed Grosjean and the Frenchman was forced off the track.
He soon rejoined and went on to finish eighth but Perez's drive-through penalty arguably cost him a points-finish. He eventually took the chequered flag in 11th place.
"He's clearly going to be watched closely at the moment and he's got to be careful in these moments," Whitmarsh told Sky Sports F1's Ted Kravitz after the race.
Perez has been involved in a number of incidents this season, notably in China and at Monaco - with both races seeing him getting too close to Kimi Raikkonen for comfort.
Perez was not penalised but after the latter, Raikkonen suggested in an interview that the 23-year-old should be "punched in the face".
He also fought with team-mate Jenson Button in the Bahrain Grand Prix. The McLarens banged wheels during the tussle, with Button telling the team over the radio to "calm him down".
"I think it was a harsh decision but if you've got a rap sheet, you've got to be squeaky-clean haven't you?" added Whitmarsh, who said in China that Perez needed to "toughen up".
"It's tough when you're a young driver and you're coming in amongst that. Inevitably the older drivers will gang up on you, they'll put you under pressure in the drivers' briefing and create an environment like that.
"That's the business. That's the sport."