Manziel flipped the bird toward the Redskins after the play that unfolded in front of Washington's bench.
Manziel said he had "words exchanged" with the Redskins and that he should have been smarter.
"I felt like I did a good job of holding my composure throughout the night, and you have a lapse of judgment and slip up," Manziel said.
Asked in his postgame news conference if he thought it was wrong, Manziel smiled before laughing.
"I mean, I didn't think it was positive," Manziel said, before adding he couldn't blame it on distractions, repeating he had simply lost his composure.
Manziel was not penalized, though he could have been for unsportsmanlike conduct or taunting.
The NFL no doubt will review the tape, and Manziel will be subject to an $11,025 fine. He can appeal his first fine, and it can be limited to 25 percent of a weekly check of close to $6,200.
"It did not sit well," Browns coach Mike Pettine said. "I was informed of it after the game and it's disappointing. Because what we talk about is being poised and being focused -- that you have to be able to maintain your poise."
The gesture occurred with 2:28 left in the third quarter.
"That's a big part of all football players, especially the quarterback, that we have to keep our composure," Pettine said. "So that's something that we'll obviously address with him."
On a second-and-7 play, Manziel dropped back, rolled left to escape the rush and threw across his body just before reaching the sidelines. The pass to Jonathan Krause fell incomplete.
Manziel may have heard something from the home bench, because as he trotted back to the huddle in the nationally televised game he extended his middle finger over his right shoulder toward the bench.
Brian Hoyer, who is competing with Manziel for the starting quarterback job, didn't seem impressed by the gesture.
"You've got to know the cameras are always on you," Hoyer said.
It wouldn't have been the first time Manziel was mocked by the Redskins.
Linebacker Brian Orakpo, who called the middle-finger gesture "hilarious," celebrated a teammate's sack of the quarterback in the first quarter by giving Manziel's Drake/money gesture, for which he is well known.
After forcing the Browns to punt with Manziel at quarterback, Orakpo stopped near the yard marker in front of the Redskins sideline and again gave the money sign.
Manziel had struggled throughout the game -- going 5-for-13 for 49 yards and one sack before the gesture.
He completed the drive after the gesture with a touchdown that came on a short drop pass that Dion Lewis ran into the end zone.
"I should have been smarter," Manziel said. "The cameras were solidly on me. I need to be smarter about that."
Information from ESPN NFL Insider Adam Schefter was used in this report.
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