Oviedo will have an operation on Monday to repair the double fracture caused to his left leg by the right boot of Stevenage midfielder Simon Heslop.
Several Everton players turned away in horror at the sight of Oviedo's left leg bent almost to a right angle on Saturday and he is now highly unlikely to play again this season.
Oviedo made only one Premier League start last term, but he has been enjoying a regular run in the side under Roberto Martinez.
The Costa Rican, who scored the winner against Manchester United last month, looked set to play a key role in Everton's push for Champions League qualification, but now he will have to endure a long and hard road back to full fitness.
"We came to win and we went ahead but then that horrible thing happened to Bryan and he is the main concern for us," Naismith told Everton TV.
"This was probably the first time in his Everton career where he has had a run of games and he has shown his potential.
"Everyone has been able to see what he has got and everyone in the team will be looking out for him now."
Oviedo attempted to hook the ball away from under Heslop's feet as the Stevenage midfielder was about to shoot.
But when Heslop swung his right boot at the ball he made contact with Oviedo's outstretched leg instead and it was clear from the player's reaction that a break had occurred.
Lucas Akins said Heslop was "upset" at causing the injury to Oviedo, but the Stevenage striker believes his team-mate should not take any blame.
"There was nothing malicious in it. It was just a freak accident," Akins said.
"He pulled his leg back to shoot and Oviedo has come in to try to block it and he has just kicked his foot.
"It wasn't a nice thing to see. It is horrible when you look at the leg and you see it's just dangling off. It was absolutely horrendous, definitely the worst thing I have seen in my career.
"We all wish him a speedy recovery.
"Simon obviously was a bit upset by it, but he is not coping too bad and obviously the lads are supporting him."
Given that he already had seven players out through injury, losing Oviedo is a big blow for Martinez - especially with Everton's next game being against Liverpool on Tuesday night.
But the Spaniard can take encouragement from the way his team so easily avoided a fourth round upset at the home of League One's bottom side on Saturday.
Naismith scored twice in the first half to give Everton some breathing space before substitutes John Heitinga and Magaye Gueye rounded off the win.
Naismith, who started up front ahead of the rested Romelu Lukaku, hopes he has played himself into contention for the Merseyside derby.
"I grew up playing up front and I have played there recently for Scotland," Naismith added.
"The manager says he is going to play me more there. I got my chances against Stevenage and I put them away so I have shown him that I can do it.
"Hopefully that has given him a thought for future games.
"We haven't got the biggest squad. We have got a lot of injuries so everyone has to play their part and I did mine against Stevenage thankfully."
Source : PA
Source: PA