On the heels of their Black Thursday, the 49ers awoke Friday to discover there are no holiday bargains on effective NFL offenses.

That means they are stuck with their current model, which looked outdated and in desperately in need of repair in a 19-3 loss to the Seahawks on Thursday night.

The wretched performance inspired what must be a professional-sports first in the social-media age: Twitter criticism from the owner and general manager’s daughter.

CEO Jed York apologized to the fans for the “unacceptable” performance and presumably wasn’t referencing a defense which allowed one touchdown. It was widely viewed as a denouncement of York’s offensive-minded head coach, Jim Harbaugh, whose team managed as many points as turnovers.

Meanwhile, Trent Baalke’s daughter, Cass, took aim at the offensive coordinator in a since-deleted tweet: “Greg Roman can take a hike … the 49ers don’t want you no more.” (Trent Baalke issued an apologetic statement today).

And you thought you had a miserable holiday with your dysfunctional family.

The 164-yard Thanksgiving effort certainly cast more doubt on the beyond-2014 futures of Harbaugh and Roman with the team. The more pressing issue: Can those two principal characters help fix the offense with the 49ers (7-5) likely needing to finish the regular season with four straight wins to reach the playoffs?

The season-ending stretch will include dates against the Cardinals and Seahawks, who rank second and fourth, respectively, in points allowed this season. Recent history doesn’t bode well: The 49ers have averaged 8.5 points en route to posting an 0-2 record against Seattle and Arizona this season.

Whatever the necessary fixes are, they don’t appear obvious. On Thursday, the members of the league’s 23rd-ranked attack had no explanation for what caused them to average 3.2 yards per play, or fail to gain more than 16 yards on any of their 51 offensive plays.

“We just didn’t play well,” said quarterback Colin Kaepernick, who later offered, “We just didn’t execute.”

Wide receiver Anquan Boldin? “Lack of execution, like I said earlier,” he said.

Even running back Frank Gore, who offers routinely offers thoughtful and substantive answers, seemed to be at a genuine loss. Gore has termed the team’s collection of offensive talent the best of his 10-year career.

“I know we have the players,” Gore said. “Things just aren’t happening for us and I don’t know why. We need to look at ourselves as a whole and see what is going on. It’s tough.”

Kaepernick was given a tough assignment Thursday: Beat the Seahawks without using your legs.

After he had 130 rushing yards and averaged 11.8 yards a carry in a 23-17 loss to Seattle in the NFC title game, the 49ers didn’t call a designed quarterback run, according to Pro Football Focus. Kaepernick had three scrambles that gained 17 yards, which accounted for 10 percent of their offensive total.

The Seahawks’ response: Thank you.

“We know that if we keep him in the pocket, it is hard for him to beat us throwing the ball,” linebacker K.J. Wright said. “When he can run and pass, be multi-dimensional, that is when we have problems with him.”

Defensive end Michael Bennett was asked to account for Kaepernick’s lack of running.

“I think that it was more his choice,” Bennett said. “He wanted to throw the ball more than he wanted to run. He had some lanes but there is probably a lot of pressure on him to be able to be a passing quarterback. He did that.”

And he did it poorly in another mistake-filled performance against Seattle.

Kaepernick arrived with just one interception in his previous 142 attempts, but he tossed two picks on 29 attempts Thursday. Kaepernick has nine interceptions in 146 career attempts against the Seahawks. He has 15 interceptions in his other 1,031 attempts, including the playoffs.

On Thursday, Kaepernick’s two interceptions came on errant throws that were corralled by cornerback Richard Sherman, who gleefully gave the index-finger-to-his-lips signal to the crowd after his second pick in the fourth quarter.

“The second one was pretty entertaining,” Sherman said. “I was laughing the whole time because I told their sideline if they throw it my way, I would end the game. And they threw it still. Way to be. Way to be, those guys.”

The 49ers, of course, have endured Sherman’s mocking in the past, most notably after Seattle’s 23-17 win in last season’s NFC title game.

Following that game, York also took to Twitter to express his disappointment. The tone of that message, however, reflected pride in his team, not disgust.

“Thx #49ersFaithful for cheering us on this season,” York wrote. “I’m sorry we couldn’t get it done for you tonight … Thx to our guys for fighting so hard.”

Twitter: @Eric_Branch