Macron, who became France's president earlier this month, added: "We need to show that we won't make small concessions, even symbolic ones, while not overdoing things either".
Mr Macron told the Journal du Dimanche newspaper his approach to the encounter had been about getting respect.
The bombing in Manchester struck a chord among leaders, including French President Emmanuel Macron who drew on his own country's experience of several jihadist attacks that have killed more than 230 people since 2015. Their knuckles then appeared to turn white with their jaws clenching and faces tightening.
Weighing in on the tense exchange between the two world leaders, body language expert and retired Federal Bureau of Investigation counterintelligence and counterterrorism operative Joe Navarro said that President Trump's behavior may indicate he does not understand the meaning of a handshake - particularly when meeting other political leaders.
Cue laughs from leaders including German Chancellor Angela Merkel and North Atlantic Treaty Organisation chief Jens Stoltenberg as Mr Macron found his arm wrenched about by a smiling Mr Trump.
While the French ambassador, Gérard Araud, did not reveal what he told the Macron, Capehart and another guest jokingly told him that he should discuss Trump's handshake with Macron. Politics, via their news site, describes President Trump's "ever-growing book of weird handshakes" as just spawning a "new chapter" in France today.
The handshake made headlines, both for its length and the apparent intensity between the two leaders, both of them relative newcomers on the world stage.
"Did you warn him about Trump's handshakes?" my philanthropist friend asked.
The next day at the G7 summit in Sicily, Italy, Mr Macron attracted attention for his friendly interactions with Canadian Prime Minister Justin Trudeau.
However, a source in the French delegation said Macron had repeated the EU's position that the terms of the divorce must be first.
Trump has said the deadly attack in Manchester on Monday showed the threat had to be met and defeated but faces pressure from Britain after key details of the investigation were leaked in the USA press.