Young, who entered Sunday's game against the Cleveland Indians with 1,998 career hits, sent slow rollers down the third-base line for singles in the fifth and seventh innings off Indians starter Josh Tomlin.
"I don't care. I really don't," Young said about they way he reached the milestone. "People asked me that beforehand. Yeah, I would've loved to taken it 500 feet to opposite field, but it really doesn't matter to me. At that point in the game we were losing, I had two strikes on me and I was trying to make contact. I'll take it anyway I can."
The Rangers rallied for five runs in the eighth inning to beat the Indians, 5-3.
Manager Ron Washington said the infield hits just showed another part of Young's all-around game.
"He can run also," Washington said. "You got to get them all kinds of ways. You don't get that many hits without getting them anyway possible, and tonight he got them like that."
Young becomes the 12th player with 2,000 hits for one of MLB's 14 expansion teams since 1961 and the first for the Rangers franchise.
He said he was glad to reach the milestone in front of the home fans.
"They've seen good plays, they've seen errors, they've seen hits and they've seen punchouts," he said. "They've seen all of me so I was very excited to have it happen with them. Obviously I've very appreciative of the support and if there's good feelings towards me. It's definitely a two-way street, and I feel the same way towards them."
Twenty-two active players have reached 2,000 hits. Young did it in his 1,621st career game, all with the Rangers.
"He's been consistent and he's showed up every day and played," Washington said before Sunday's game. "It just shows that he's a grinder. Health has a lot to do with it. He stayed healthy. Undoubtedly he had to learn how to play through some mishaps to get to this point. ... The good ones do. They always do, and he's a real good one."
Young is the franchise's all-time leader in a number of categories, including hits, games played, at-bats and runs.
Washington thinks Young, 34, has a chance at 3,000 hits, a level reached by only 28 players. New York Yankees shortstop Derek Jeter, the only active player with that many hits, reached the milestone July 9.
"If he can stay healthy and stay away from missing time, Michael will figure how to get 180 to 200 hits every year," Washington said.
Young doesn't plan to slow down.
"I don't plan on retiring anytime soon so it was kind of a next step," he said. "I'm going to keep going hard and make sure I keep my priorities right, which is show up to the ballpark and do everything I can to help the team win games."
Master Tesfatsion is a reporter for ESPNDallas.com.