The three-times world beater knows from the time that Coulthard drove for the team headed by his son, Paul, that he often lost the battle in his head rather than on the track.
"If I was in David's position, I would be getting my head together," Stewart said. "He had a couple of off-days in Brazil and you just cannot afford to have them at this level of sport.
"It is all mind management. It was a similar situation when David was driving for us in Formula Three. If the car was right and everything else was good then David was unbeatable. But if something was slightly off then he could be beaten.
"I don't think he is any slower than Mika. David demonstrated in the opening race in Australia that he was just as quick, if not quicker. But there is no doubt that Mika totally controlled the Brazilian Grand Prix. There were no team orders there and David was trying as hard as he could.''
Coulthard admitted after being outperformed by Hakkinen in Sao Paulo - to trail the Finn by eight points after two races - that he was not yet at his best.
The McLaren duo are expected to turn Sunday's Argentinian Grand Prix into an Easter Day parade as they bid for a fourth consecutive one-two finish in a run that stretches back to last year.
But Stewart believes the competitive nature of Formula One will eventually see Williams and Ferrari hit back. "Nobody is bullet-proof," Stewart said. "Things change very quickly in this sport, even from a position of complete dominance which McLaren have now.''
Stewart also rejected speculation that his team's exclusive five-year deal with Ford for a factory engine was in danger from Benetton. "I have had a personal contract with Ford for 34 years and they have always honoured contracts," he said.
All 90,000 tickets have been sold for British Grand Prix day at Silverstone on Sunday, 12 July, circuit officials announced.Reuse content