The San Francisco 49ers, in contrast, had reason to celebrate after beginning the Jim Harbaugh era in impressive fashion.
Romo and the Cowboys hope to bounce back from a disappointing defeat while the 49ers look for their momentum to carry over Sunday at Candlestick Park.
Since taking over as Dallas' starting quarterback in 2006, Romo has earned a reputation for failing to succeed in crucial situations. While his career passer rating of 95.6 ranks fourth in league history, he has an 80.8 mark while going 1-3 in the postseason.
The result of last Sunday night's meeting against the New York Jets had far less significance than a playoff game, but it served as another painful reminder of Romo's inability to come up big with the game on the line.
After fumbling three yards from the end zone, Romo threw an interception late in the fourth quarter that led to the Jets' go-ahead field goal in Sunday night's 27-24 defeat - the Cowboys' first loss in 248 games when leading by at least 14 points in the final period.
Despite the turnovers, Romo's teammates were quick to defend him.
"That's not the rap in this locker room," linebacker Keith Brooking said of Romo, who finished with 342 passing yards and two touchdowns. "Who cares what everybody else thinks? ... That wasn't Tony Romo's loss. ... That's not the way this team looks at it.
"I'll take that guy over anybody in this league. Y'all might think I'm crazy, but I'm telling you right now, he's going to have an all-time year... I've seen enough football to know the guy's ready for the next level."
While Romo looks to regroup, the 49ers (1-0) will try to build on their 33-17 victory over defending NFC West champion Seattle last Sunday.
Playing in his first game since suffering a season-ending hip injury on Nov. 29, running back Frank Gore was held to 78 total yards, but Ted Ginn Jr. returned a punt and a kickoff for touchdowns in a 59-second span to seal the win for Harbaugh in his NFL coaching debut.
"Just to win for coach Harbaugh...to be part of it is really something special," said David Akers, who made four field goals. "This is a franchise with great history and, obviously, the last some years have been a little on the down side.
"We are trying our best to change that. It takes time, but (Sunday) was a good start."
San Francisco, which hasn't posted a winning record since going 10-6 in 2002, was pleased with its victory, but its inability to move the ball consistently was surely a concern.
Alex Smith, who ran for a touchdown, completed 15 of 20 passes for just 124 yards and Braylon Edwards - making his 49ers debut - hauled in three receptions for 27 yards. Michael Crabtree, meanwhile, caught just one pass for four yards in limited action as he remains slowed by an injured left foot.
Crabtree's status for Sunday remains uncertain, but Edwards and tight end Vernon Davis could be in for a big day against a banged-up Dallas secondary.
Orlando Scandrick is expected to miss three-to-four weeks with an ankle injury, and Mike Jenkins missed parts of Sunday's game with a shoulder injury. It is unknown if Jenkins will be available in this one.
The Cowboys (0-1), who signed journeyman cornerback Frank Walker on Tuesday, could also be without two-time Pro Bowler Terence Newman again as he continues to deal with a groin injury suffered early in training camp.
Newman and receiver Dez Bryant, who played through a thigh injury in the opener, both missed practice Wednesday.
While Dallas is hoping its injury-plagued secondary recovers quickly, it held the Jets to just 45 yards on the ground and could make things difficult on Gore.
Gore, who has managed just 3.2 yards per rush in two career games in this series, was limited to 26 yards on 14 carries during a 35-22 loss in Dallas on Nov. 23, 2008, during which Romo threw for 341 yards and three TDs.