Reid also disparaged Army Gen. David Petraeus, head of Multinational Forces in Iraq.
But Reid, whose comments to bloggers first appeared in The Politico, also told reporters: "I think we should just drop it."
Reid's admission came as reporters peppered him with questions about Pace and Petraeus, overshadowing a Capitol Hill press conference designed to highlight Democratic attempts to improve fuel economy and energy efficiency.
Reid said he told Pace face-to-face recently that he had performed poorly as an adviser on the conduct of the Iraq war.
"I believe that General Pace would not be if he had come forward to be reappointed the chairman of the Joints Chiefs. It wouldn't have happened and I'm not going to get into what I said or didn't say. There is a long list of people including Senators (Carl) Levin and (Jack) Reed and others who have talked about General Pace long before I did. I think we should just drop it. The fact is, he's not going to be the chairman of the Joint Chiefs, for which I'm happy," Reid said.
Asked if Reid considered Petraeus incompetent, Reid responded, "Not as far as I'm concerned."
Reid ripped Petraeus for an interview published in Thursday's USA Today describing progress in Iraq.
"I have high regard for General Petraeus. When I was in Iraq, he was responsible for training the Iraqi troops. He told us it was going great. As we've looked back, it didn't go so well," Reid said. "I was a little disappointed, to say the least, today reading USA Today newspaper, where he's saying things are going fine, kids are playing soccer. The truth is, you look at another newspaper and look at a different page of USA Today, the bloodiest three months of the war has been since the surge took place," Reid said.
Prior to Reid's remarks, White House spokesman Tony Snow told reporters that he hoped what he had read about Reid is "not true, because in a time of war, for a leader of a party that says its supports the military, it seems outrageous to be issuing slanders toward the chairman of the Joint Chiefs and also the man that is responsible for the bulk of military operations in Iraq.
"Indeed, Senator Reid has at some point declared the war lost and also has declared the surge a failure, even though it has not yet been fully enacted," Snow said, adding that Reid should apologize.
Snow said Bush had decided not to reappoint Pace, not because of mistrust over the handling of the war, but so as to avoid a "spectacle" on Capitol Hill.
"What they decided to do was to spare the general and also the American public the kind of spectacle that I think in some ways explains the low esteem with which people regard the entire political class in Washington, especially Congress," Snow said.
"I think the president has constantly stood up for General Pace, and has also made it clear that he values his 40 years of service to this country," Snow added.
The decision not to reappoint Pace to a second term was based not only on Democratic objections to the chairman but to Republican desires to avoid a fight on Capitol Hill, FOX News learned Thursday.
Senate Armed Services Committee Ranking Member John Warner, R-Va., revealed that he and fellow committee Republicans had conveyed to Defense Secretary Robert Gates that Pace would be too easy a target for Democrats to rehash past mistakes and issues regarding the Iraq war.
"I made it clear that it was the president's decision. I had worked successfully with Pace," Warner said. "But I supported the secretary's conclusion that we have to look forward and not go back over and over the issues of the past, like WMD and the like," Warner said of the fight over the weapons of mass destruction.
"The secretary made a tough but wise decision," Warner said.
Bush has nominated Adm. Mike Mullen to be the next chairman of the Joint Chiefs. Gen. James E. Cartwright, currently the commander of the Strategic Command, was nominated as vice chairman. Cartwright would succeed Adm. Ed Giambastiani, who is retiring in part because the chairman and vice chairman generally come from different branches of the Armed Services.
FOX News Major Garrett and Trish Turner contributed to this report.