Minutes after replacing Lacina Traore in attack in the fifth-round tie at Goodison Park on Sunday, Naismith latched onto Neil Taylor's short back-pass before slotting past Gerhard Tremmel to put the hosts back in the ascendancy.
His second-half strike followed by a Leighton Baines penalty secured the Toffees' progression after debutant Traore saw his fourth-minute opener cancelled out by Jonathan de Guzman's header.
Naismith left the field for the closing stages of the game with a head injury following a collision with Jordi Amat, but Martinez says that it was a precautionary move to bring off the Scotland international.
"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."
Martinez's side will now face Arsenal in the quarter-finals as he looks to become the first manager to secure back-to-back FA Cup trophies with two different clubs.
He added: "We are very satisfied because all you are looking for is a win to get into the next round.
"We were a little bit anxious and feeling the role of playing at home and expecting to get into the next round and we were too cagey with our possession allowing Swansea to get well organised.
"The second half was very different, we controlled the game, creating good opportunities and limiting Swansea to very little."
Meanwhile, Martinez also admitted his delight with Traore as the striker bagged the opener in his first Everton appearance since joining on loan from Monaco.
"For Lacina Traore to play 60 minutes was a real success," he said.
"I thought he coped with those instructions for the team off the ball really well and he scored within four minutes of his new career.
"It is a beautiful sign for the future. Then to see Steven Naismith continue with his good moment of form, taking his goal really well."