NEW YORK -- In his first 16 starts of the season -- all with the Chicago Cubs -- Ryan Dempster gave up as many as six runs one time.

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In his first three starts since being acquired at the trade deadline by the Texas Rangers, the 35-year-old has already given up eight runs -- twice.

So, Ryan, about that transition from the National League to the American League ...

“Too much is made of that,” Dempster replied after getting shelled again, this time to the tune of eight runs on nine hits in six-plus innings during an 8-2 loss to the New York Yankees on Monday night in the Bronx. “I know how to make pitches. It just comes down to executing. And tonight, I paid for my mistakes.”

Nick Swisher made sure of that. With the bases loaded, one man out and the Rangers ahead 2-0 in the third inning, Swisher tattooed a 1-0 hanging slider from Dempster into the second deck in right field, giving the Yankees a 4-2 lead they’d never relinquish.

Swisher’s ninth career grand slam -- the 10th career salami allowed by Dempster (one shy of Kenny Rogers’ MLB record of 11) -- served as the lowlight during a 31-pitch third inning during which Dempster faced 10 batters and surrendered five runs on five hits while walking two.

“Every time he made a mistake up in the zone, they didn’t miss it,” Rangers manager Ron Washington said.

Early on, Dempster’s fastball, slider and splitter were sharp. In fact, he retired the first six Yankees he faced. But it all fell apart from there.

As a Cub, Dempster compiled a 2.25 ERA. As a Ranger, he has compiled an 8.31 ERA.

“There’s always pressure every time you pitch,” Dempster, who fell to 0-4 with a 7.62 ERA in five career starts against the Yankees, replied when asked about pitching in a pennant race. “You gotta execute pitches. It’s a simple formula, and I’ve just got to do a better job of that.”

The entire Rangers pitching staff does. They may be the two-time defending AL champions, but they’re going to have to do a better job in that department if they want to make it a three-peat.