Further demonstrating his concern for Meghan, the actor then went on to recall a time when he advised the soon-to-be royal to remove a faux engagement ring she was wearing while shooting scenes for Suits before she leaving the set.
"We were about to get out of the car and I said 'Don't get out, give us the ring," he revealed. "There's paparazzi down the street. If a photograph got out with you with a ring on it, it would explode all over the world'."
Due to a clash in schedules, Pierce was unable to attend the Duke and Duchess of Sussex's historic nuptials but revealed that he was "irrationally happy" for the couple the time.
Since marrying into The Firm, the newly-titled Duchess has come under scrutiny across the globe with a number of tabloids plastering her personal life across their front page spreads. Last week, the new mother spoke out for the first time about the immense pressure she has been under since wedding Prince Harry in a now-viral interview.
During ITV documentary Harry & Meghan: An African Journey, which followed the couple's latest royal tour, the 38-year-old admitted that she is "not OK".
"Any woman especially when they are pregnant, you're really vulnerable and so that was made really challenging," she told anchor Tom Bradby. "And then when you have a newborn - you know. And especially as a woman, it's a lot. So you add this on top of just trying to be a new mum or trying to be a newlywed."
"Also, thank you for asking because not many people have asked if I'm OK," Meghan continued. "But it's a very real thing to be going through behind the scenes..."
In a bid to regain some control, the Duke of Sussex recently revealed that the couple are seeking legal action against British tabloid The Mail on Sunday for publishing a private letter from Meghan to her father, Thomas Markle.
"Unfortunately, my wife has become one of the latest victims of a British tabloid press that wages campaigns against individuals with no thought to the consequences - a ruthless campaign that has escalated over the past year, throughout her pregnancy and while raising our newborn son," he said in a moving statement.
"I have been a silent witness to her private suffering for too long. To stand back and do nothing would be contrary to everything we believe in."