Hamilton finished second at Silverstone after a first-lap incident with Kimi Raikkonen, for which the Finn received a 10-second penalty, and was furious to have missed out on the chance to win his home race.
Drivers who finish on the podium are required by F1 regulations to conduct a post-race interview almost as soon as they get out of the car for the TV broadcast, but the Brit stormed past pundit Martin Brundle instead of stopping to answer questions.
And while former McLaren driver Coulthard stopped short of criticising Hamilton’s actions, the Scot did point out that the obligations exist for a reason.
“These guys are under the spotlight, under pressure and under different demands on their time. They have good days and bad days just like the rest of us,” said Coulthard, speaking to Express Sport at an event to celebrate DTM’s return to the UK at Brands Hatch on August 11-12.
“Maybe it was not about the incident. If he’d won the race it would have been different, elation maybe.
“We want them to be individual and a reflection of their real selves but then when they are and it doesn’t suit us then we say ‘oh, he didn’t even talk to us’.
“The reality of being a professional sportsman is that you’re being paid to do a load of things you don’t really want to do – which is anything that isn’t driving.
“But to be professional, you have to recognise how your money comes to you.
“It comes through sponsors, media outlets promoting and fans turning up and watching.
“You can’t turn your back on that.”
On Thursday, Mercedes finally announced a new contract for Hamilton, whose current deal expires at the end of the year.
The two-year commitment is reportedly worth £60m, rising to £80m with performance-related bonuses, and will see him stay with the team until the end of 2020.
If the 33-year-old wins every title up to that point, it will take him level with the legendary Michael Schumacher as a seven-time world champion, a long-held ambition of Hamilton’s.
But Coulthard reckons this year’s race is still very close and is not completely under the driver’s control.
“I think what will decide this championship will not only be [Hamilton’s] input but also the tyres, we’ve seen some circuits suit Mercedes and some suit Ferrari, who have also made a big step forward on the ending which has brought them into another window,” Coulthard added.
“Are Mercedes able to respond without affecting reliability? That’s a pressure they haven’t been under of late.
“The risk they have is that if they run the engines in a higher state, they might not finish. If they don’t finish, they take themselves out of the championship.
“The difficulty with being in a dominant position is you naturally become more conservative because you have more to lose.
“When you’re attacking, all you’re getting if you lose is more of what you had in the past. It changes the psychology.
“But that’s why it never stays the same and other teams come up.”