BEREA — Go ahead, joke all you want about Baker Mayfield taking his first step to the Hall of Fame.

Todd Haley does.

"I know a lot of people are carving the bust for Canton already," the Browns offensive coordinator said. "I know he set the bar high. I don't know that every week's gonna go like that."

Mayfield put up a 100.1 passer rating and led a game-winning 75-yard touchdown drive that ended with two minutes left. The Browns won 21-17 to improve to 1-1-1, and now Mayfield is preparing for his first NFL start, at Oakland, on Sunday.

"Baker played great ... it was phenomenal stuff," Haley said. "He gave us a chance to win, but at the same time, there's a process."

Haley, 51, has coached in the NFL since the mid-1990s, but he has never been in a situation like this, taking a top-of-the-draft quarterback into his first NFL start this early in his career.

He said his closest comparison is having nurtured young Tony Romo in Dallas, although Romo was a third-year pro when he became a Cowboys starter. Another big difference: Romo was undrafted out of Eastern Illinois. Mayfield was a Heisman Trophy-winning No. 1 overall pick from a college that went to the BCS final four.

Yet, Haley said, "It's a good comparison, because they're similar in attitude and football savvy."

Haley is sympathetic to former starting quarterback Tyrod Taylor, saying the 30-year-old veteran basically didn't have a chance against the New York Jets last week on "Thursday Night Football."

"While Tyrod was in there, I don't care who it was, getting the quarterback hit on the first five plays, through no fault of his own, it's gonna be a struggle," Haley said. "Our offense has to execute better earlier in games."

The Browns went three-and-out on Taylor's first series, then got a first down on the second series only because Taylor scrambled for 22 yards on third-and-10. The Browns soon punted, then followed that up with three more three-and-outs.

Taylor's final play was a sack by linebacker Avery Williamson, after which he disappeared into the medical tent. His stat line: 4-of-14 for 19 yards, with three sacks. Mayfield went 17-of-23 for 201 yards, taking one sack.

How much of Taylor's rough night is attributable to getting nailed early and often?

"One hundred percent," Haley said. "I know we're all very excited about Baker, but I want everyone to know Tyrod has done nothing but a tremendous job. He put us in position to win the first two games.

"We've made too many mental errors. If we make some of the errors we've made in all three games, it's not going to matter who's playing. It was not a fair position to put Tyrod in."

Coach Hue Jackson said he hasn't decided whether 36-year-old Drew Stanton or Taylor will be the backup to Mayfield on Sunday against the Raiders. Stanton has been Mayfield's primary sounding board from a player-mentorship perspective, while Taylor has focused on being ready for games.

"I took some flak for saying this is the best quarterback room I've been around," Haley said. "Kurt Warner texted and said, 'What?' "

Haley suggested the Browns debated the topic of whether Mayfield should replace Taylor in the wake of beating the Jets. He left no clue about whether there was any serious opposition to elevating the rookie, while continuing to stick up for Taylor in a sense.

"I'm gonna choose not to talk about any of the internal stuff," Haley said. "Lastly about Tyrod, he came in and has been a leader from day one ... of this group, of this entire building. It wasn't all this excitement and prettiness then. He was a big part of getting this thing going in the right direction."

Haley acknowledged a difference in style between Taylor and Mayfield.

"Baker's more of a gunslinger," he said. "He's going to rip it around a bunch. We've got to make sure those are going to the right place most of the time.

"Tyrod is a completely different kind of quarterback."