Vettel was slapped with a five-second penalty for cutting the corner at Turn 3 and then almost forcing Hamilton into the wall.
The German defended his pole position magnificently to cross the chequered flag in first place.
But Hamilton was just 1.4 seconds behind meaning after the punishment was added to Vettel’s time, the Mercedes driver secured the win.
However, Coulthard disagreed with the decision as he wants to see drivers pushing each other more aggressively on the track.
“I don’t agree with their decision,” Coulthard told Channel 4.
“Putting yourself inside the cockpit and I can just about remember what it is like at that corner. I have been across that grass.
“He made a mistake and the unforced error was there and Lewis got himself in a position to potentially take the lead.
“But an unforced error in Monaco doesn’t mean that you get the lead because there is barriers.
“The unforced error led to the fact there was a concrete wall so there was no way past.
“I just don’t think five seconds is the right thing. Whatever happened to racing?
“We find ourselves subduing the racing with all these penalties.”
Meanwhile, Sky Sports pundit Jenson Button also had a similar opinion of the incident.
“It’s sad – it’s disappointing when there’s a proper fight on out on track between two great, multiple world champions, and then the stewards are able to come in and take that away from us viewers,” he told Sky Sports.
“It’s a shame. For me, it’s a racing incident.
“Yes, Seb made a mistake, but you’ve got to realise he’s doing over 100mph here, you can’t just stop the car and stay off the circuit.
“He’s had a snap, come back, and it doesn’t deserve a penalty for me, personally. I don’t think. But it’s a regulation, and they’re decided to take it.”