The Spaniard confessed that the Toffees' comfortable outing at the Lamex Stadium was overshadowed by the Costa Rican's misfortune
The Costa Rica international suffered a suspected broken ankle when he launched into a slide tackle with his side 2-0 up.
Oviedo was rushed straight to hospital and Martinez has already admitted he is resigned to losing the left-back - who scored the winner when the Toffees beat Manchester United at Old Trafford earlier this season - for a considerable period of time.
"A real negative today is an unfortunate injury and we end up with Bryan picking up a bad injury", he said.
"We need to give him as much support as we can because he's had a terrific season and I've been so impressed with his level and the way he's been playing in different positions.
"He's a really important player in the group and we all wish him a speedy recovery now and we hope everything goes well, because he clearly deserves it."
Despite the massive injury blow, Martinez was pleased with his side's performance and hailed their attitude.
"If you want to see a professional performance, that's as professional as it gets," he added.
"We had to defend well and I thought the concentration in dead-ball situations was a real test and we always looked a real threat on the counterattack.
"We looked clinical in front of goal so as a performance it's as good as it gets.
"The incident with Bryan obviously affected everyone. Those injuries really give you a bad taste but overall from the fans to the type of the game it was a real proper cup tie and a professional performance from our point of view."