"John, his staff and players are focused on the three fixtures that remain this season," the club said.
The club statement added: "There have been two days of frank dialogue with John Carver and senior players.
"All parties accept responsibility for the current situation but are determined, together, to ensure this club retains its Premier League status."
The Magpies - who host West Brom on Saturday - are 15th in the Premier League table, just two points above the relegation places. They also face QPR away on 16 May and West Ham at home on 24 May.
They were in the top half of the Premier League when manager Alan Pardew left for Crystal Palace at the turn of the year.
Carver was placed in charge until the end of the season but has lost 12 of his 17 games in charge in all competitions.
Carver accused defender Mike Williamson of deliberately getting sent off against Leicester on Saturday.
Captain Fabricio Coloccini and keeper Tim Krul were reportedly involved in a lively row on the coach after the game, according to the Daily Telegraph.
That poor form has caused widespread anger among the St James' Park faithful, with Carver compelled to ask the club for protection from his own fans - and then inviting two supporters around for a "cup of tea" after an incendiary exchange during the team's loss to Swansea last month.
There were widespread press rumours that Derby boss and ex England manager Steve McClaren would take over as early as Friday now Derby are out of the play-offs. But this speculation has proved wide of the mark as owner Mike Ashley sticks with Carver.