The toffees were stunned when Sebastian Bassong headed in a last minute equaliser in Saturday's 1-1 draw against Norwich at Goodison Park.
Oviedo has admitted that David Moyes' side need to up their concentration in order to make their Champions League dream a reality.
"The goal was very disappointing. It made it difficult for us. We need to look at it and see what happened because we can't afford to keep conceding late goals." He said in the Liverpool Echo.
"We've conceded too many in the last five minutes. Yeah, we've got injuries but that's not an excuse; we just need to work harder because we want Champions League.
"We have the team for Champions League football. We have good players but we need to start concentrating better and defend much better from free-kicks and corners."
The Cost Rican was also quick to defend his team-mate Nikica Jelavic, who missed a number of chances to seal the win, saying: "The responsibility shouldn't be just with Jelavic. The whole team should be scoring goals.
"Everyone has missed good chances. He is a very good player and he's important for us. I looked at Jelavic before I signed and knew what a fantastic player he is. We need to help him and be better in midfield and defence too.
"Everton are one of the top teams in the country and we need to start showing it again. I am so happy I could play well and help the team. It's very difficult in the Premier League.
"The matches and games are tough. I need to keep preparing the same and keep focused. We need to get it out of our heads because the next game is coming in a few days.
"We need to be prepared for that. When I play, I always try to help the team and play well, for me and for Everton, of course."