The Scotland international left the pitch with concussion before the end of the match, after being caught in the head by Jordi Amat's arm, not remembering he had scored - his fourth in five matches - or won a penalty in the 3-1 victory.
Martinez said the player would be monitored over the next 24 hours but did not believe there was a serious problem.
"Naismith is okay. We will check him over the next 24 hours as he had a bit of delayed concussion with the knock," said the Spaniard.
"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."
On-loan Monaco forward Lacina Traore had got his Everton debut off to a perfect start with an instinctive backheel after just four minutes but Jonathan de Guzman levelled things up with a powerful header before Naismith, capitalising on Neil Taylor's backpass, and Leighton Baines from the penalty spot secured a place in the quarter-finals.
"We are very satisfied because all you are looking for is a win to get into the next round," added Martinez.
"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.
"For Lacina Traore to play 60 minutes was a real success. I thought he coped with those instruction 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."
Swansea caretaker manager Garry Monk defended his decision to make eight changes, with a Europa League tie against Napoli in midweek.
"When you have got seven games in 21 days it is impossible to play the same 11 in every game," he said.
"I can only judge the boys on the week I have had and their attitude has been magnificent, every one, from the first day I said everyone would play and I was true to my word.
"It is a squad game. Everyone seems to be amazed when there are rotations.
"With Europe you have to have that rotation. Every side I pick is a team to try and win the game."