"He's not behind at all," manager Alex Cora said.
Although Martinez will be Boston's primary designated hitter, he is expected to get time in the field. With the Red Sox playing split-squad games, he played left field and batted cleanup.
Facing Twins right-hander Jake Odorizzi, Martinez twice flied out.
"Seeing the ball, just going up there and trying to slow the ball down as best as I can and swing at strikes," Martinez said. "Really, that's all I was really worried about -- just get a pitch over the plate and put a good swing on it.
"It felt good. It was fun. You don't realize how much you miss something until you can't do it and you haven't been able to do it for a while. So it was fun to get out there."
The AL East champion Red Sox announced Feb. 26 that they had signed Martinez to a $110 million, five-year deal. The 30-year-old hit a combined .303 with 45 home runs and 104 RBIs last season in 119 games with Detroit and Arizona.
In his first game for Boston, Martinez hit behind Hanley Ramirez, who was serving as the DH. It's a combination the Red Sox hope will add punch to a lineup that finished last in the American League with 168 home runs last season.
"He was designated for assignment four years ago [by the Astros, at the end of spring training in 2014], and now he's going to hit in the middle of the lineup for the Boston Red Sox, with a team that has a chance to win the World Series," Cora said. "There's no coincidence that he's been successful the last few years because he found it and he keeps working on it."
Martinez said he typically likes to get 60 to 80 at-bats in the spring, including Grapefruit League and minor league games, to prepare for the season.
Despite the delayed start to Martinez's spring, Cora said he believes the big hitter is on pace for the season opener March 29 at Tampa Bay.
"It's a spring training game, so he needs his reps," Cora said. "But to see him out there, actually to see him around, spend time with him, it's a lot different than the last week.
"We've been on the road so much since he signed, we haven't been able to connect. So to have him in the lineup, have him in the dugout, that's good, not only for me but for everybody."
Martinez knows there are big hopes for him, but he isn't letting that affect him.
"I feel like you guys have the expectations, the fans and the media," he said. "Really, I'm just going to go out there and play my game and do what I've been doing for the last four or five years.
"As far as the pressure and stuff goes, I'm just going to try to go out there and play my game. Obviously, ignore it, stuff like that. Obviously, playing in Boston, it's a big market, so there's going to be a lot more, but I think it'll be a good test of handling it."