EAST RUTHERFORD, N.J. -- For the third straight week, New York Jets quarterback Aaron Rodgers was left to explain a loss in which his team missed an opportunity to win the game on its final possession. This time, he seemed more frustrated -- and concerned -- than ever.

"We need to get going," Rodgers said Monday night after the Jets -- in their first game under interim coach Jeff Ulbrich -- dropped to 2-4 with a 23-20 loss to the Buffalo Bills at MetLife Stadium. "This was a golden opportunity. Some games you win in the NFL and some games you give away. This was a giveaway."

Not only was he critical of the Jets' performance, but Rodgers questioned the officiating, too. The teams combined for 22 penalties and 204 yards, including 11 for 110 by the Jets, who suffered the same issues under former coach Robert Saleh.

"It seemed a little ridiculous," Rodgers said of the officiating. "Some of (the calls) seemed really bad, including the roughing-the-passer on me [by AJ Epenesa]. That's not roughing the passer. You might as well play Sarcastaball [a reference to the TV show 'South Park'] if we're going to call those things. And I thought the one on [Javon] Kinlaw wasn't roughing the passer, either."

Rodgers also bemoaned a "phantom holding call" on tackle Tyron Smith that nullified a scoring run by Braelon Allen that would've given the Jets a 27-20 lead in the third quarter. They got no points out of it, as Greg Zuerlein missed his second field goal of the night.

The Jets, who fired Saleh last Tuesday, capped a tumultuous week with a performance that smacked of so many others. There were too many penalties and too many blown opportunities.

Under new play caller Todd Downing, who replaced the demoted Nathaniel Hackett, the offense managed to produce 393 total yards, but it went 1-for-4 in the red zone. One of their two touchdowns was a miracle play -- a 52-yard Hail Mary to Allen Lazard at the end of the first half, which closed the Bills' lead to 20-17.

"Demoralizing" was how wide receiver Garrett Wilson described the penalties, mistakes and squandered chances. "We have to find a way to score touchdowns because I don't want to keep feeling like this."

The Jets have lost three in a row by a combined total of 10 points, the latter two games ending with a Rodgers interception on their final possession. For the first time in his 20-year career, Rodgers has a losing record after six games.

"It's frustrating," he said. "I'm here to win those games."

This time, Rodgers got the ball at his 30 with 3:43 remaining in the game -- 70 yards away from a touchdown that might have vaulted the Jets into a first-place tie with the Bills (4-2). The last time the Jets shared first place after Week 6 was 2012 -- the NFL's longest drought.

There was no Rodgers magic.

The drive imploded with a sack and two Jets penalties (one offsetting), ending with a third-and-16 deep ball to Mike Williams that was picked off by Taron Johnson at the Bills' 18 yard line. Rodgers intimated that there was a miscommunication between him and Williams, who suffered a head injury on the play.

Rodgers (23-for-35) threw for a season-high 294 yards, including two touchdowns, but he wasn't happy with the overall execution by the offense. He said the attention to detail must improve. He could improve, too. In the red zone, he was only 3-for-8, including four passes that were either tipped or defended.

"I thought we were going to have a big night on offense," he said. "Again, this should have been a 30-plus point game on offense, and this shouldn't even be a conversation."

Owner Woody Johnson fired Saleh with the hope of creating a new energy under the fiery Ulbrich. It worked -- for a short time. After Rodgers' Hail Mary to Lazard -- the fourth Hail Mary touchdown of Rodgers' career -- the Jets went into halftime with the momentum. But they left it in the locker room, managing only a field goal in the second half.

Now they're in danger of falling out of contention.

"We are by no means out of this thing. By no means," Ulbrich said. "I know the character of that locker room. I know the way we will respond. ... We have to start stacking these weeks of exceptional preparation. I promise you it will start to pay off on Sundays."