"I argued that everyone should get an up-or-down vote but we lost that battle," Cornyn told reporters just after a vote to end debate on Liu's nomination failed 52-43.
"Now what they want is for any Republican nominee, a nominee of a Republican President, to require 60 votes, whereas a nominee from a Democratic President get 51, and that's just not fair," Cornyn said. "So I think the same rules should apply. They basically rewrote the rules, and I'm saying we'll play by the rules that they wrote."
"I think this is an exception, an extraordinary circumstance," Cornyn told TPM. "I don't think this is the norm. I don't think you could say that because of what happened on this nominee, that's gonna happen routinely, in fact I can assure you it wouldn't."
Liu has faced opposition from Republicans because they say he's too liberal. Supporters say the real reason for GOP opposition is because of his young age and potential as an eventual nominee for the Supreme Court.
A bipartisan group of senators who averted a judicial crisis back in 2005 -- known as the "Gang of 14" -- previously agreed that judicial nominees shouldn't be blocked unless there were "extraordinary circumstances." Cornyn and other Republicans said that was the case with Liu.
Democrats bashed the GOP's opposition to Liu, who would have been the only Asian-American serving in the Ninth Circuit court, which has a 40 percent Asian population.
"It is an outrage that Senate Republicans have blocked the nomination of Goodwin Liu, an exceptionally well-qualified and mainstream judicial nominee who is widely admired, even by leading conservative legal scholars," Sen. Barbara Boxer (D-CA) said in a statement.
"I believe the ramifications of this Republican filibuster will be deeply felt in California and across the country," Boxer said. "When we deny a judicial nominee of Professor Liu's caliber - a man of intelligence, integrity and dignity - we weaken our nation's legal system."
Senate Judiciary Chairman Patrick Leahy (D-VT) said that the "partisan filibuster of Goodwin Liu's nomination is another example of Republicans' shifting standards on judicial nominations."
"Professor Liu deserved better treatment than the Senate has allowed," Leahy said. "All Americans suffer from this filibuster."
Sen. Orrin Hatch (R-UT) was the sole "present" vote on the vote to end debate. He told reporters it was the "honorable" thing to do because he wrote a law review article making the case that judges should not be filibustered. But he doesn't blame fellow Republicans for blocking Liu's up-or-down vote.
"They filibustered our judges, they set the standards. Nobody should try to make a case against Republicans for trying to vote against cloture or in other words to sustain the filibuster because the standard was set by the Democrats, they filibustered our judges," Hatch said.
"Democrats set the standard," Hatch said. "We passed more judges for this President and for Clinton than they ever did for ours."
"If they're trying to make the case that they're righteous and Republicans are not, that's a joke," Hatch added.