McKay went 0-for-4 with four ground balls in Monday's 6-3 victory over the Orioles. He hit eighth in the Rays' lineup as the team's designated hitter.
"I feel like I had good at-bats, obviously not the results you want," McKay said. "But making solid contact is putting you in the right direction. Now, it's trying to find the holes in the defense and get your first hit out of the way."
McKay pitched six scoreless innings in his Major League debut Saturday against the Texas Rangers. He is only the fourth player since 1913 to begin his career with a start on the mound and as a non-pitcher within his first two games, according to STATS.
"He certainly looked the part," Rays manager Kevin Cash said. "I don't know when the next opportunity will be, but he'll get back out there, and we'll get that first hit eventually here and keep him rolling from there."
McKay is scheduled to pitch at home against the Yankees on Friday. New York is 7-2 against the Rays this season.
Tampa Bay is 49-36 this season. The Rays trail the first-place Yankees by 6 1/2 games in the AL East Division.