Newton completed 23 of 32 passes for 221 yards with two touchdowns while also rushing for 50 yards and a touchdown as the Panthers improved to 4-3.
The Buccaneers are mired at 0-7 and Schiano is under added pressure after the team also lost five of their last six games last season, while local media have reported his players were upset at his authoritarian coaching style.
Another ineffective display on their home field, where they failed to score a touchdown until late in 'garbage time' of the final quarter, will only intensify the pressure with a heavy portion of the crowd sporting signs asking for him to be sacked.
"It doesn't affect me," the under-fire coach said.
"You can sit there and cry about it and feel sorry for yourself but that ain't going to help anything.
"People are certainly entitled to their opinion. Here's the thing, my whole career, player and a coach, you get up in the morning and work as hard and as smart as you can, it usually puts you to bed tired and you get up and do it again and that's the way I do it."
Schiano said the only way forward was to stick together and keep looking to improve.
"We are doing the best we can, our coaches and players, stick together, sometimes it doesn't go your way," he added.
"You have to keep doing it, look for new ways to make as better, and hopefully go get a win in Seattle (next week).
"We just made some errors that are going to keep you from winning games. Those are the things you get paid to do as a coach, to get your team to perform those things, so it certainly falls on me."
The Panthers started strongly with an impressive 15-play, 70-yard first drive, resulting in a touchdown to tight-end Greg Olsen.
Tampa Bay responded with a field goal but Carolina went right back to work, driving 80-yards on their next possession in six plays, culminating in a 12-yard touchdown run from DeAngelo Williams for an early 14-3 advantage.
The Buccaneers added another field goal to go to halftime trailing 14-6.
Newton rushed for his touchdown early in the third quarter period before opening the fourth with a three-yard pass to Mike Tolbert to blow the score out to 28-6.
A late field goal padded the Panthers score while Tim Wright caught a 10-yard touchdown pass from quarterback Mike Glennon for the Buccaneers with under three minutes left.
Glennon completed 30 from 51 pass for 275 yards and the late touchdown, though his numbers were improved in the final few minutes of the game with the result already decided.