Carver was undertaking media duties amid an unexplained absence from Alan Pardew, who has been hotly linked with the vacant manager's job at Premier League rivals Crystal Palace.
Pardew's right-hand man was not allowed to discuss the manager's future after goals from Papiss Cisse, Ayoze Perez and Jack Colback earned Newcastle the spoils against Roberto Martinez's inconsistent side at St James' Park.
But the Newcastle number two believes the spirit garnered after recovering from Arouna Kone's fifth-minute opener for Everton will stand the Tyneside club in good stead.
Carver told BBC Sport: "It's nice to get a result after a tricky few games. We got off to a bad start but looked a different team after the first five minutes.
"We took the game to Everton and got a deserved win. When you have had a run of games were you haven't won, it's very important to get the win.
"We've got back-to-back home games with Burnley coming up. They had a great result today so we know it's going to be a difficult game."
The game was not without controversy, with Cisse fortunate not to be sent off for elbowing Seamus Coleman when Everton were 1-0 up.
Carver claimed not to see the incident, adding: "All I saw of the incident was Seamus Coleman lying on the floor. I have not had a chance to look at it."
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