TAMPA — He did not even wait for the referee to administer a coach's version of the last rites.

Dirk Koetter was already heading toward his final goodbyes before Matt Bryant's winning field goal had landed Sunday afternoon. The Bucs coach strolled to midfield, shook a few hands and then walked off the turf without breaking character or stride. The only thing missing was the wail of a bugle.

It was better this way. Another loss seemed appropriate, another heartbreak seemed fitting. No sense complicating the future with last gasps or false hopes.

The loss of a job should always be clean and decisive.

And in Koetter's case it was merciful and proper.

It's not that his three years as a head coach in Tampa Bay had been disastrous. Koetter had done a better job than at least a half-dozen Bucs coaches, if you want to get technical. But 48 games later, here was the one question that had no happy answer:

Where was the evidence of better days?

It wasn't on the defensive side of the ball, where the Bucs were among the least effective teams in the NFL. And it was harder and harder to have faith in an offense that always seems to look better on the stat sheet than the scoreboard.

For two years, this has been a team in search of ways to lose, and Sunday's 34-32 mindblower against Atlanta was no different. Penalties, turnovers, collapses, failed conversions? Ding, ding, ding, splat!

"We couldn't finish games,'' said center Ryan Jensen. "Whether that's on the coaching or the players, I don't know. It's just the way it was.''

Honestly, it's on the coaches and players both.

But the Glazer family has invested too much in this roster for a complete overhaul, and so the sensible thing to do was to find a new coach to pace the sidelines.

Unlike some previous years when the Glazers had practically taken out Help Wanted ads before the end of a season, there was little noise about Koetter's future from the owner's suite before Sunday night. Maybe that was because there are fewer obvious candidates on the horizon, or maybe it's because their preferred choice is still walking on some other sideline.

Either way, they knew what they were doing before notifying the world three hours after Koetter had left the field on Sunday. They may have known it when the team ran into a wall in September, they probably knew it when Koetter was late firing defensive coordinator Mike Smith in October, and they darn sure knew it when they looked at thousands of empty seats in November and December.

And the fact the Bucs remained largely competitive did not help Koetter's case. This is not a weak roster that occasionally wins due to a coach's ingenuity. It's a decent team that can't get over the hump.

And the Glazers know what that looks like.

Remember, they fired both Tony Dungy and Jon Gruden after 9-7 seasons. Quick ascensions are not uncommon in the NFL, and the Glazers are betting this is one of those opportunities.

And though they have made some missteps in the past — Hey there, Greg Schiano! — the Glazer family has also been extremely bold when it comes to looking for head coaches.

They chased Steve Spurrier. Twice. They once wanted Bill Parcells and Jimmy Johnson, too. They tried to lure Chip Kelly out of college, and tried to trade for Steve Mariucci in San Francisco. They even attempted to lure Ralph Friedgen from Maryland, and paid a ransom to get Gruden.

Right now, it feels like we're due for one of those chases again.

The owners have made an incredible investment in quarterback Jameis Winston in terms of draft, money and time, and all indications are they're not giving up on him yet.

That means spending even more money to ensure Winston gets the best coach available, and going after a hot, new coordinator doesn't seem to fit the current circumstances.

So does that mean chasing Michigan coach Jim Harbaugh? That makes more sense than Oklahoma's Lincoln Riley, who doesn't have the same NFL pedigree.

Does that mean chasing former Packers coach Mike McCarthy? That makes more sense than giving former Broncos coach Josh McDaniels a second chance.

What seems apparent is the Glazers still have faith in the players assembled on this roster. Otherwise, general manager Jason Licht would have followed Koetter out the door.

So expect a coach with a big name, a fancy resume and no margin for error.

Contact John Romano at jromano@tampabay.com. Follow @romano_tbtimes