The Scotland internationalist and former Rangers striker 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 goal in five matches - or won a penalty in the 3-1 victory. Martinez said the player would be monitored over the next day or so but did not believe there was a serious problem.
"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 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 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.
Garry Monk, the Swansea City caretaker manager, 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 XI in every game," he said. "I can only judge the boys on the week I have had and their attitude has been magnificent. From the first day I said everyone would play and I was true to my word. With Europe you have to have that rotation. Every side I pick is a team to try to win."