The 50-year-old took charge of the Magpies in January following Alan Pardew's departure, and it wasn't long before the club plummeted into a relegation battle.
The North-East outfit suffered eight defeats in a row from March 4, but they were able to clinch Premier League survival with a 2-0 win over West Ham United on the final day of the season on Sunday.
"John deserved the win against West Ham because he has worked really hard with the team," Janmaat told The Chronicle. "He tried everything. I feel sorry for him. We let him down in games and it can't happen again."
It is not yet known whether Carver will be handed the manager's job on a permanent basis.