The team also has no plans to change kickers before the Browns play in Washington, coach Hue Jackson said Monday.
This latest drama came after Parkey went 3-for-6 in his Browns debut. Parkey's missed 46-yard attempt on the final play of regulation led to a loss and came after Parkey was rushed onto the team over the weekend.
"I think it's unfair just to dump it all on him," Jackson said.
Parkey joined the Browns after Patrick Murray hurt his knee in practice on Friday. On the chance someone might call, Parkey kicked on his own Friday afternoon near his home in Jupiter, Florida. He heard from the Browns, then flew to Cleveland on Friday night.
He went to the facility Saturday morning and had no time to practice before he got on the plane with his new teammates to play the Dolphins. His first warm-ups came before the game. During the game he made field goals of 46, 48 and 38 yards, but he missed kicks of 41, 42 (off the upright) and 46 yards (the potential game-winner).
"Everybody says 'Well, that's the kicker's job'; well, it is his job," Jackson said. "But normally a guy has a job, he's been around his employer a little bit. He's been around his teammates a little bit. So it was tough, it was tough circumstances.
"It was unfortunate. If he would have made it, we'd be celebrating right now. But he didn't."
Every one of the misses went left, which might indicate Parkey was anxious and trying too hard. After the game, he merely said, "They all missed left, so ... aim right."
Parkey kicked in only three games in 2015 before going on injured reserve with a groin injury. In his rookie season in 2014, he went to the Pro Bowl. When Murray was injured, the Browns had a choice of a young player like Parkey or a veteran like Robbie Gould, who was cut by the Bears before the season started.
"We felt good about watching [Parkey] kick on tape. We felt good about everything that he was doing," Jackson said. "We felt he was the best of the group, and we all made that decision together."
Jackson said any chatter that the coaching staff preferred Gould should be dismissed. The Miami Herald reported from league sources that special-teams coach Chris Tabor wanted Gould, but the front office took Parkey, in part because he cost less. Tabor was assistant special teams coach in Chicago from 2008-10, when Gould was the Bears' kicker.
Jackson said the Browns picked Parkey because he was "the guy that we wanted." The team has somewhere near $50 million in salary-cap room, and it did now know what Gould would cost because it decided on Parkey. But if Gould would have signed for the veterans minimum, which seems likely, the difference between Gould and Parkey would have been less than $500,000.
"Any decision that's made here by the football team we make together," Jackson said. "I felt very comfortable. And if there's anything that comes out of this building it should come from me, not from anybody else. If I didn't say it, I guarantee you nobody else has any right to ever say anything about 'we should have had this guy' or 'somebody wished they had that guy.'
"We took the guy that we wanted. That's Cody Parkey. That's the guy we put on our team and that's the guy who kicked for us."
The Browns' M.O. through this point of the season has been to favor younger players who can grow together under Jackson. Murray fit that mold before he was injured.
Gould is 34, Parkey 24. The past two years when Parkey was in the league in Philadelphia, he made 35-of-40 kicks (87.5 percent), 4-for-4 from 50-yards plus. Gould was 42-for-51 (82.4 percent), 7-for-10 from 50 yards plus.
But Gould had a stretch last season when he went 2-for-5. That included misses of 40 and 36 yards in an overtime loss to San Francisco. The 36-yard try could have won the game on the last play of regulation. The next game, against Washington, Gould missed a 50-yard kick with 1:45 left that would have tied the game. At the end of this preseason, Gould also missed two extra points in the finale against the Browns. The Bears decided to part ways with him, and Gould has not been picked up.
The Browns stand by the decision to sign and keep Parkey.
"I challenge any of us to come in here on a flight on late Friday night, wake up and meet the coach for a second and get on another flight and head to Miami and not know really a lot of your teammates, but some," Jackson said. "Walk out and kick in pregame, and then kick in a game, where you attempt five of these feel goals. Not two, not one, but five.
"That's a lot of pressure. And then here's the game-winner. Hitting you right in the face. That's a tough situation."