CINCINNATI >> The Bengals’ quest to end their long streak of playoff futility has gotten a lot tougher.

A 20-17 overtime loss in Denver on Monday night most likely cost the Bengals (11-4) a chance for a first-round bye in the playoffs. If the Broncos (11-4) win at home against San Diego (4-11) next Sunday, they’ll get the bye.

Instead of having a week off to let Andy Dalton’s broken thumb heal, the AFC North champions would host a playoff game and then have to win two more on the road in order to reach the Super Bowl — a much tougher road.

This one really stings.

“Obviously, we knew what we had in front of us, the opportunity to get the bye,” defensive end Carlos Dunlap said.

Several Bengals starters are injured and were hoping for a week of rest. Receiver A.J. Green is playing with a sore back. Tight end Tyler Eifert missed the past two games with a concussion. Safety George Iloka missed the past two games with an injured groin. Cornerback Adam “Pacman” Jones is playing with an injured right foot.

Plus, a bye would have given Dalton another week for the broken bone in his right thumb to heal. It’s been two weeks since the injury. The Bengals are hoping to get him back for the playoffs, but the likely first-round game complicates it.

“It’s tough,” Green said. “We have a lot of guys banged up, so we could have really used that bye. All we have to do is go out there and take care of next weekend, and hope for the best.”

The Bengals host Baltimore (5-10) on Sunday. They can still get a first-round bye if they beat the Ravens and the Broncos lose, or if they lose and the Broncos lose and the Chiefs win.

The way that they lost in Denver was as disappointing as anything. AJ McCarron made his second NFL start and was impressive in the first half. He led the Bengals on two long touchdown drives to open the game against the league’s top-ranked defense, and got them in position for a field goal that Mike Nugent missed.

McCarron’s performance in the opening half was enough to reassure Cincinnati that it can still win in the playoffs if Dalton’s unavailable. McCarron was 12 of 17 for 119 yards with a touchdown and no sacks or interceptions as Cincinnati led 14-3.

“He played great,” Green said. “He did everything right.”

The Broncos played more zone coverage and blitzed more in the second half, when McCarron was 10 of 18 for 81 yards with a pair of sacks. He fumbled a shotgun snap in overtime, sealing it.

“We put ourselves in a position to win the ballgame and I failed the team,” McCarron said. “That is what it comes down to.”

McCarron hurt his left wrist while trying to recover the fumble and was scheduled for tests on Tuesday. It’s his non-throwing hand, so he’s expected to start against the Ravens. The backup is Keith Wenning, who was a fifth-round pick of the Ravens in 2014 and spent the season on their practice squad. He was promoted from the Bengals’ practice squad after Dalton got hurt.

The Bengals are left in a position of needing a lot of help to get a bye and improve their chances of ending the sixth-longest streak of playoff futility in NFL history. They haven’t won a playoff game since the 1990 season.

“It just leaves all the ‘what ifs’ out there,” safety Reggie Nelson said. “I mean, back to square one.”

Notes: Players had Tuesday off as they recover for the Ravens game. … The Bengals finished 6-2 on the road, matching their best mark for a season. They’ve done it four times in their 48 years. … Cincinnati fell to 3-17 in Monday night games on the road. They’ve dropped their past six since winning in Cleveland in 1990.

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