The Northern Irishman was annoyed to be put on the clock with his French playing partner Gregory Bourdy early in the round and he also said he did not think the bunkers around Muirfield were totally fair.
"They told us on the fourth tee that we were two and a half minutes behind schedule," McDowell told reporters.
"All right. Fine, we got off to a slow start. We were cutting it very close."
As they walked on to the fifth tee the pair were told they were four and a half minutes out of position and were going to be put on the clock.
"Surely we're allowed to get off to a bad start?," the former US Open champion said.
"There's a difference between slow play and bad play. So they put us on the clock for one hole. And we got to the next tee and they said you're off the clock now.
"So it's like make up your minds, guys. That's not really slow play regulations. It was a tough start. And on the clock on the fifth hole is a bit out of order really."
McDowell, 33, spoke to the referee and expressed his frustration which bubbled up again when the subject of the Muirfield bunkers was brought up.
"The sand is very soft and there's lots of it," he said. "They're a real hazard this week. I think bunkers should be penal at times.
"But there's no doubt these bunkers have been created for the balls to stick around the lips. They're not particularly deep in places so they've decided to make them hazards in a different way."
McDowell believes it is a lottery which way the ball goes into the bunkers.
"For such a fair golf course like this one, it brings an element of chance into it which I don't love," he said.
McDowell, who finished at six over par, was aware that his comments might be construed as sour grapes because he did not play well.
"It's really just an observation," he said. "I've probably had about 10 trap shots in three rounds and I'd say two of them have been normal. There's no doubt there's an argument for how much of a hazard should a bunker be."
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