Goals to Ross Barkley, Romelu Lukaku and Leon Osman saw Everton triumph at St James' Park on Tuesday, while the home side were held scoreless for the sixth time in their past nine Premier League matches.
The likes of Luuk de Jong, Papiss Cisse and Yoan Gouffran failed to convert early in the game as Newcastle started strongly but after wasting those opportunities, the hosts were made to pay when Barkley struck a fine goal after a thrilling slaloming run from Everton's defensive half.
Carver, in his final game in charge of Newcastle before manager Alan Pardew returns from a touchline ban, was left frustrated by the lack of cutting edge in the forward third.
"We had two or three chances early on in the game," the assistant manager said.
"Probably the best start we've had for a long time to a game but they were so clinical in their finishing and we weren't again."
Newcastle had 54 per cent possession and 16 shots to Everton's nine but were unable to avoid their second loss in three league games.
When Gerard Deulofeu teed up Lukaku for Everton's second goal just seven minutes after half-time, the visitors looked to be comfortably heading towards victory, although Carver felt Osman's third in the 87th minute was unfair on Newcastle.
"I've got to be honest. I thought 3-0 was a flattering scoreline (for Everton)," Carver said.
Carver added he was looking forward to having Pardew back after the 52-year-old completed his three-game touchline ban on Tuesday for headbutting Hull City midfielder David Meyler.
"Yeah, it'll be great to have him (Pardew) back because he's the manager and I know my role and he knows his role in the football club," Carver said.
"Just being in and around the dressing room, he has a different idea at times than me and we bounce things off each other.
"I mean I've done that with (first-team coach) Steve Stone but, in all honesty, the manager's got a lot more experience than Steve and it'll be nice to have him back."
