Bisaccia, previously the special teams coordinator, has served as interim head coach since October when Jon Gruden resigned.
After steading the ship he led the Raiders into the postseason with four straight wins down the stretch but the team's hopes were ended in the Wild Card round on Saturday.
The home Cincinnati Bengals held on to triumph 26-19 and celebrate a first postseason win for 31 years, leaving the Raiders still waiting to end their own drought which has run since 2002.
Carr, who only has one year left on his contract, threw an interception on fourth-and-goal with 12 seconds remaining after earlier finding Zay Jones in the end zone as his team attempted to recover from 14 points behind.
The quarterback completed 29 of 54 passes and hopes it is Bisaccia who returns in 2022 as the Raiders begin to turn their attention to next season.
"I think we can all think that he's the right guy," said Carr, per ESPN.
"He has proven that people listen to him. Our team listens to him and I love him so much, I'm thankful for him.
"All those things will be decisions that I don't make, I don't get to make. I just play quarterback, but with everything that went on, if you really look at what happened, all the pieces missing, everything that changed.
"Yeah, he held it together."
As well as Gruden's exit, Carr discussed the release of leading receiver Henry Ruggs III and a host of injuries suffered by Raiders receivers and offensive linemen in a tumultuous year.
"You go on and on and on and on, and that's just offense," he said.
"The fact that that staff kept everything together and kept us competitive and kept us finding ways to win football games, I think that's what our organization is about, right?
"So, we'll see what happens. We know what we want to have happen. But, again, we're Raiders. We're going to play football, but we just hope it, obviously, we hope it's for somebody special."
Asked about his own future, Carr cited his agent's strong relationship with the team and added: "Lord knows there's been a lot of things to communicate about, right?
"When the time comes, I never want a face-to-face. I'm going to play quarterback, but my message will be talked about.
"I'm not going to go to dinner and say, 'We have to do something.' I'm not that guy. I'll let my voice be heard, but in a different way."
Star pass-rusher Maxx Crosby also spoke up for Bisaccia after the game.
"If it was up to me, I think everyone in the world knows what my decision would be," he said. "One of the best people I know.
"I love Rich. You know, I'm biased, obviously, but he's a great coach, he came in and got us to 10 wins. We came on the road, on a short week, and gave Cincinnati everything they could handle."
Bisaccia would not be drawn on his job chances, nor did he discuss the controversial Bengals touchdown which saw Tyler Boyd catch a Joe Burrow pass seemingly after a whistle had been blown by game officials.
"I'm just thinking about those guys in that locker room that played the game with their heart and soul out there like that and had a chance to win at the end," Bisaccia said.
"We just ran out of time. We did some uncharacteristic things with some penalties and gave up some drives and didn't capitalise when we had it in the red zone at times. So it just didn't go our way."
On the TD controversy, he added of the officials: "I think that's a good crew.
"There's a lot of things that went on in the game both ways. I got enough problems with my job, I can't do the officiating, too."
The Raiders' Darren Waller had seven catches for 76 yards, while Josh Jacobs had 83 on the ground at Paul Brown Stadium.