Cowboy's defensive end, DeMarcus Lawrence, could be seen hitting an object that was about to hit him, though he later told reporters it was aimed at officials.
When star quarterback Dak Prescott was asked about the fans' actions, he initially expressed his disappointment when he thought they were directing their anger at the players.
Given the circumstances surrounding the end of the game, it might be understandable why Cowboys fans were frustrated.
Despite all the offensive talent the team has, Dallas struggled to move the ball against the 49ers - the Cowboys had 11 ball possessions, seven of which ended without points.
But with six points behind and with just over 30 seconds on the clock, Prescott had the opportunity to correct.
He managed to move the attack to San Francisco's 41-yard line with 14 seconds left, after which the 49ers called a timeout to stop the clock.
But instead of throwing after the end zone - and with no timeouts left - Prescott ran 17 yards on a designed quarterback run.
When the Cowboys and 49ers tried to get in position so Prescott could stop the clock by throwing the ball to the turf, referee Ramon George also ran to catch the ball.
George collided with Prescott before the quarterback could stop the clock and time ran out before QB could get snapped off.
At his post-match press conference, Prescott said the intended game was something he and his teammates had practiced.
That wish, however, was not fulfilled and the Cowboys were knocked out of the playoffs by the first time they asked.