CINCINNATI — Chris Henry would run right past the cornerback and catch the long pass in stride. Chad Johnson would burst into the end zone and start the show — another never-before-seen touchdown celebration that might involve the ball, the pylon or a fake Hall of Fame blazer.

Carson Palmer? Sure looked like a Hall of Famer.

Those were the days.

The Bengals’ offense was a high-tech marvel, ranked right up there with Peyton Manning’s prolific bunch in Indianapolis. They got to the playoffs in 2005 — a huge breakthrough for the forlorn franchise — by throwing the ball over defenders’ heads.

Now, they can barely get in the end zone.

They didn’t score in their season opener against Denver on Sunday until there were 38 seconds left. Then, they gave up a tipped, 87-yard touchdown catch by Brandon Stokley that gave the Broncos a 12-7 win. The wacky play has gotten all the attention, overshadowing the offense’s latest dreary day.

‘‘Pure luck,’’ Chad (formerly Johnson) Ochocinco said on Wednesday. ‘‘With our offense, we shouldn’t have been in that situation anyway.’’

They’ve been in it a lot the last few years.

The offense ranked sixth overall in 2005, when Palmer had his breakout season. He led the NFL with a team-record 32 touchdown passes and tied the NFL record by compiling a passer rating over 100 for nine straight games.

Now, they’re trying to dig out from the bottom. The offense’s overall ranking has slipped every year since 2005, to No. 8, No. 10 and, finally, No. 32 last year, when Palmer missed a dozen games because of an elbow injury.

The reason? It’s always something.

Injuries and attrition have caught up with the offense. So have other defenses, which rarely give the Bengals a chance to throw long. Blend in a dollop of self-destruction, and the equation balances out.

They’re just not the same.

Palmer’s torn elbow ligament and tendon were the main factors last season, causing him to miss a dozen games. Without him, the whole offense fell apart.

He missed three preseason games because of a sprained left ankle and acknowledged that he felt a little rusty at the outset Sunday. Before the touchdown drive, the Bengals had only 65 yards and one first down in the second half.

His receivers couldn’t see much difference.

‘‘Carson was fine,’’ Ochocinco said. ‘‘Everything that was thrown was catchable. I know the ankle bothered him in the preseason, but there was nothing wrong with his arm. If he could drop back in a wheelchair, he could get the ball to us.’’

A lot of it was on the guys catching and blocking.

Cincinnati had four dropped passes — two by Laveranues Coles — and several inexcusable penalties. Twice, they got flagged for having linemen downfield on a pass. Ochocinco was called for holding and for pushing off on cornerback Champ Bailey to get open.

Also, the Bengals botched a snap on a field goal attempt and had a tipped pass intercepted at the Denver 20, coming up empty on two first-half chances.

‘‘It’s the thing that kills offenses,’’ offensive coordinator Bob Bratkowski said after practice Wednesday. ‘‘They become their own worst enemy. Not only do they have to beat themselves, they have to beat the other team. And right now, we’ve got to make sure we’re not having to beat ourselves.’’

They’re also failing to take advantage of the few chances they get to throw the ball deep, which has been an emphasis in the offseason. Since their huge season in ’05, the Bengals have seen a steady diet of ‘‘Cover-2’’ defenses — two safeties dropping deep to take away the long pass.

The way to beat the ‘‘Cover-2’’ is to run the ball and complete intermediate passes, forcing the safeties to get closer to the line. The Bengals haven’t done either consistently enough to force the defenses’ hands. The result is an offense stuck in a very small box.

On Sunday, Denver allowed only one completion longer than 20 yards, Ochocinco’s catch-and-run that went for 34.

‘‘They weren’t going to let the ball go over their heads,’’ Palmer said. ‘‘They played two deep safeties, as deep as a safety that I’ve ever seen. They lined up 25 yards deep and started backpedaling. They weren’t going to let the ball go over their heads.’’

Opponents have adjusted. So far, the Bengals haven’t.