The visitors were already two goals down at Goodison Park when, in the 59th minute, Coloccini fouled Aaron Lennon and was dismissed by referee Martin Atkinson.
Substitute Ross Barkley added to earlier goals from James McCarthy and Romelu Lukaku and Newcastle have now won just one of their last six league outings.
Coloccini's red card could see him banned for three matches, which would see him miss the Tyne-Wear derby with Sunderland early next month.
"I've looked at it four or five times from different angles and it's not conclusive, but that might just be the footage we have," Carver said.
"When it happened, from the reaction of the Everton players I thought it must have been a red card but when I came in at full-time and had a look at it, it was difficult to decide.
"I'll look at it again, if it's worthy of a sending off I'll accept it. If it's not then we'll appeal but in all honesty I tried to look at it and I still wasn't convinced.
"If it was worthy of a red card then he deserves a three-match ban but if it wasn't then we'll have a look at it."
