CHICAGO (CBS) – White Sox GM Kenny Williams was on “Hit and Run” 670 the Score this morning said the team’s rebuilding effort will not come at the expense of trying to win right away.

After last year’s dismally disappointing season saw the Sox miss the postseason for the third straight year, Williams acknowledged the team was starting a rebuilding phase.

But in an interview with Barry Rozner and Matt Spiegel on “Hit and Run” on Sunday, Williams insisted he never meant that the Sox would sacrifice their goal of winning while they rebuild.

“What people didn’t hear, Barry, was what I said immediately after I said we would be in a rebuilding phase,” Williams said. “People did not hear or pay attention to the very next sentence. I said, but we will not have a domino falling effect.”

LISTEN: Kenny Williams on Hit and Run

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Other than losing starter Mark Buehrle to free agency and trading right fielder Carlos Quentin, closer Sergio Santos and reliever Jason Frasor for prospects, the roster is largely unchanged from last year.

Williams acknowledged that he sought to make deals to bring in young prospects in exchange for some of the team’s veteran players, but said he did not get the kinds of offers he wanted. So, rather than bringing in prospects that he didn’t think would have the impact he wanted, he focused on bringing in a few new prospects while keeping veterans who could help the Sox win now, like starter John Danks, who got a long-term contract.

“We did what we’ve done for the last 12 years. We tried to get, you know, enough young players into the stream so that we can protect our future, but … we felt like we still have an equal chance to win, as we did before we subtracted some of the pieces that we did,” Williams said.

“It’s not to terribly difficult to understand,” Williams said. “We went into the offseason and we tried to exhaust ourselves with looking at possibilities, like we usually do, to get ourselves better; and, generally that means more on the veteran-laden front.”