The Scotland international replaced earlier scorer Lacina Traore just after the hour-mark before putting the Toffees ahead in the 65th minute when he pounced on a defensive error from Neil Taylor.
That goal came after Jonathan de Guzman had equalised for the Swans and it preceded Leighton Baines' 72nd-minute penalty, won by Naismith, which sent the Toffees on their way to a quarter-final clash with Arsenal.
After the match, Martinez was full of praise for Naismith who had to come off late following a head clash with Jordi Amat.
"Naismith is okay," he said. "We will check him over the next 24 hours as he had a bit of delayed concussion with the knock.
"He was okay and then all of a sudden he became dizzy and he couldn't remember what was happening and we couldn't take any risks.
"He said he didn't remember he scored so I told him he scored from 40 yards! He is a gem of a boy, an incredible footballer and I am just pleased he is enjoying his football.
"He has played in different positions but when he is central he is at his best, he was instinctive, a real threat and he is enjoying his football.
"I want him to carry on doing that. We hope he will be fine and be able to join training this week."
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