Cal came into the season with an optimistic goal of earning a bowl berth for just the second time in seven years.

Now, achieving that goal would take something downright magical.

After Saturday’s 37-7 loss to UCLA in front of a homecoming crowd of 45,889 at Memorial Stadium, the Bears will need to win three of their final six games to earn bowl eligibility.

They’ll likely be favored in just one of those contests, and three of them will be on the road, where they haven’t won as Pac-12 visitors in three years.

“The only solution is to go fight through it. That’s the only answer,” Cal head coach Justin Wilcox said after the Bears’ third straight loss dropped them to 3-3 overall and 0-3 in Pac-12 play. “… We’ve all got to be part of the solution. We’ve got to give them answers, and then, we’ve got to go fight.

“These are pivotal moments, so we’ve got to fight.”

If there’s such a thing as a must-win game at the midway point of a college football season, this was it for Cal, but the Bears didn’t play with anything close to that kind of urgency.

Cal schedule Date Opponent Time/ Result Sept. 1 N. Carolina W 24-17 Sept. 8 at BYU W 21-18 Sept. 15 Idaho State W 45-23 Sept. 29 Oregon L 42-24 Oct. 6 at Arizona L, 24-17 Oct. 13 UCLA L, 37-7 Oct. 20 at Oregon St. 1 p.m. Oct. 27 Washington TBD Nov. 3 at Wash. St. TBD Nov. 10 at USC TBD Nov. 17 Stanford TBD Nov. 24 Colorado TBD

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Instead, they were pushed around and run over by a UCLA team that entered the game 0-5 for the first time since its 1943 squad opened with seven losses and was ranked last in the conference in scoring and total yardage.

After consecutive weeks of losing via the self-inflicted wounds of penalties and turnovers, Cal simply was beaten in every facet of this one. The Bears couldn’t make true freshman quarterback Dorian Thompson-Robinson uncomfortable, couldn’t stop running back Joshua Kelley and couldn’t create anything buzzworthy on offense.

Thompson-Robinson completed 13 of 15 passes for 141 yards and Kelley ran 30 times for 157 yards and three touchdowns. Cal quarterback Brandon McIlwain was 22-for-40 for 168 yards and running back Patrick Laird had 17 carries for 94 yards and a score.

Neither of Cal’s best offensive players had a run of more than 14 yards, and McIlwain fell apart in the fourth quarter. He committed four turnovers in garbage time, giving him 11 turnovers in the past three games, including five that have been returned for touchdowns.

“It’s never going to be acceptable to give up the ball and commit turnovers, but we’re going to continue to work on it,” McIlwain said. “It’s now or never. It’s time to make a change and find a way to pick it up.”

Cal had won eight of its previous nine home games in this series, losing to UCLA in Strawberry Canyon only in 2014 during that stretch. But even in their natty Joe Roth throwback uniforms, there was little chance of the Bears making it nine of 10.

Nothing went right for Cal in the first half as UCLA pounded the ball right up the gut of the Bears’ defense for a 13-0 lead. Kelley had 19 carries for 114 yards before halftime.

As if it needed more trouble trying to stop UCLA, after trimming the deficit to 13-7 midway through the third quarter, Cal was called for both an unsportsmanlike and a targeting penalty on the Bruins’ next drive. UCLA got 15-plus-yard runs from Thompson-Robinson and Kelley, and Kelley capped the 83-yard drive with a 1-yard dive that seemed to start a torrent.

After stopping Cal on a 4th-and-1 try at the 48-yard line, UCLA picked up a key fourth-down conversion of its own. Thompson-Robinson found Kelley for a 7-yard pass in a 4th-and-2 situation, and five plays later, Kelley barreled into the end zone from a yard out to put away the game.

“At no point in the game was the offense, defense and special teams playing well together,” Wilcox said. “At no point.”

Rusty Simmons is a San Francisco Chronicle staff writer. Email: rsimmons@sfchronicle.com Twitter: @Rusty_SFChron