The Toffees' season has been something of a source of frustration for the fans, with the club's inconsistent form seeing them struggle to get out of the bottom half of the Premier League table.
However, despite sitting in 11th place they are just six points off Manchester United in fifth and a run of good form could see them shoot up the table in the final few months of the campaign.
After the Merseyside club were narrowly denied a place in the Capital One Cup final by defeat over two legs to Manchester City, Oviedo insists that Roberto Martinez's side can continue to compete on all fronts.
He told the Echo: "I think we are very close to being a side that can compete at the top of the league. The best teams work very hard, and for me we are one of the best teams.
"I have been here for over three years, and this is the best group of players, definitely. We need to work hard and look with more ambition. I think we have one of the best squads in the Premier League, but we need to demonstrate it by winning games.
"We have the team to do it. We have everything you need to win the FA Cup. It is not easy, of course, but if we are working together and playing to our maximum then we can do it for sure."
Oviedo has become a regular at left-back under Martinez in recent weeks since returning from a long-term injury, keeping Leighton Baines on the substitutes' bench.
Everton take on Bournemouth in the FA Cup fifth round at the Vitality Stadium this weekend before they return to league action a week later.