Parker says the United States and China offer the best growth prospects for the Japanese carmaker.
He says Mazda needs "to continue to provide exciting products that are relevant to consumers."
"One of the reasons our brand is not that strong in North America is we have not done that consistently over five, 10 or 15 years," he says. "We haven't delivered the quality of products that the market expects. We haven't listened adequately to the way the customer wants the product to work for them in that market.
"So the feature content and the way the product delivers for them has not been properly attuned to that customer," Parker adds. "We do a good job of that in Japan, we do a great job in Europe. But we do a less-quality job in North America."
But Parker says Mazda is improving in North America.
"Unfortunately there's this lag factor which you have to deal with," he says. "When you've disappointed customers in the past, you have to do it four times better and for probably four times longer before you can truly get them back into your showrooms."
Mazda also must do a better job of developing cars attuned to American buyers, he says.
"When we've brought good products, they have caused some level of dissatisfaction because of the way we've brought them to market and not adequately listened to the North American consumer," Parker says.
To beef up its distribution, Mazda's "whole logistics and parts availability also has to be refined and improved," he says. "Last but not least, we need to make sure that those dealerships are profitable and earn a return on their investment, so that they see Mazda as a good business."