Red Sox manager Terry Francona couldn’t hide it. While he may be happy that his players had a chance to represent their countries and play in the inaugural World Baseball Classic, he’s glad to have them back.

Catcher and team captain Jason Varitek and relief pitcher Mike Timlin returned on Saturday, after Team USA was eliminated by Mexico, 2-1 on Thursday night. Designated hitter David Ortiz and pitcher Julian Tavarez were the last Red Sox players left in the Classic, but the Dominican Republic bowed out to Cuba on Saturday, 3-1.

“Yeah, and they look excited to be back,” Francona said of Timlin and Varitek. “I think they both wanted to win, but I think they looked real happy to be back. It was fun watching [Varitek] out there just being with the guys.”

For the players, it was somewhat of a relief to be back.

“Yeah, to be with my team, there definitely is,” Varitek said. “It was an awesome, awesome experience. I think the U.S. learned a lot from it and [will] be even better prepared the next go-round.”

“It was probably one of the funnest things I’ve ever done,” Timlin said. “It ranks right up there with playing in the World Series. When we were coming into the game with Mexico and Korea, I was more nervous than I’ve ever been in my life, and that’s just prior to the game.

“I enjoyed the experience. It’s a different atmosphere, playing for your country, playing with guys that you haven’t played with before, the experience of being on the team with those guys and putting the red, white and blue on is awesome. But I’m glad to be back in camp.”

Timlin, who pitched 2 1/3 innings over three games, compiling a record of 1-0 (3.86 ERA), was not available for the United States’ game against Mexico on Thursday night after the trainers shut him down with a tired arm.

“It’s just like a tired arm, that’s all,” said Timlin, who threw a bullpen session Saturday morning at City of Palms Park and felt no ill effects. “With anything, the trainers there, you get a hangnail and they’re like, ‘OK, let’s make sure you’re clubs OK with it.’ It’s just precaution.”

Francona plans to remain cautious with Timlin’s arm.

“We planned on that anyway,” he said. “He threw on the side [Saturday] and did pretty well. We’re going to let him go down and face [Minor League] hitters Monday on the off-day and then we’ll kind of gauge where to go from there.”

Both Timlin and Varitek said while they would welcome the opportunity to compete in the Classic again, they would like to see some changes instituted.

“Get guys together a little sooner, make some adjustments, get guys some more at-bats earlier,” said Varitek. “I think we got caught so our hitters were a little overmatched timing-wise.

“I think it would be good to play some games — intrasquad, exhibition games, whatever — just get some more games under your belt.”

“[The loss is] disappointing for the fact that the talent we had, we lost,” said Timlin. “But the talent that we had at the time of the year, our timing was just off. That’s all there is to it. Our hitters didn’t have enough at-bats to have their hands right where they want.

“Pitchers were off a little bit. There were spurts where you threw the ball exactly where you want it, struck guys out, got the right ground ball, hitters have great day. But it just wasn’t enough.”

Both players suggested better places in the baseball calendar to hold the tournament.

“There’s better times in the middle of the season when everybody’s in top shape,” said Timlin. “There’s a better time after the season, after the World Series, when people are in top shape.

“Play it after the World Series, put the team together, let them practice together for a couple of weeks. Before you do something like that, they’ll already be in game shape. It won’t take guys too long to get back where they should be.”

Varitek, who appeared in three games and started two, went 2-for-7 (.286), including a grand slam March 8 in USA’s 8-6 loss to Canada, said his preparation is not behind schedule in spite of his limited playing time.

“I got a lot of work in. I just don’t have the at-bats yet,” he said. “I’ve already caught eight innings, eight intense innings. But it’s hitting us on both sides. There’s things that will benefit well, and there’s things that won’t be as well. It’ll be good to get some consistency playing.”

After playing in six playoff-caliber games, both players said their mental preparedness is ahead of their physical — for now.

“Mentally, I’m probably ahead of where I should be in my game mode,” Timlin said. “Physically, I feel like I’m a little bit behind. But it won’t take long. My timing’s just off, that’s all.”

Varitek will get a chance to catch up, starting in Sunday’s game with Bronson Arroyo pitching. | By Maureen Mullen