After booking their place in the two-legged semi-final against Manchester City in early December the Toffees managed just one league win - coincidentally against Newcastle - before Wednesday's 3-0 victory over the Magpies.
They exited the cup competition last week after defeat in the second leg at the Etihad Stadium but bounced back with a 3-0 win at League Two Carlisle in the FA Cup and then repeated the feat against the Magpies in the Premier League.
"The Capital One Cup maybe was a little distraction from the Premier League for us," said Oviedo.
"With this team that doesn't need to happen but sometimes it does.
"Sometimes it is difficult. We were very sad to lose at Man City but right now it is different.
"We need to focus on the most important thing which is the next few games. If we win the next few games we are nearer the top again.
"At the moment we are focusing on the most important thing which is the Premier League right now and the FA Cup."
While victory only moved Everton up one place to 11th in the table it at least put a healthy 11 points between themselves and their opponents, who occupy the last relegation place.
It was their first at home in the league since November and only their second clean sheet at Goodison Park all season.
Equally as importantly, unlike on other occasions recently, they did not squander their early advantage given to them by Aaron Lennon and closed out the game with two late Ross Barkley penalties.
"It was a very good game for us and to get three points was very important because the last few games we maybe lost some important points," added Oviedo.
"We were talking about being strong in the last few minutes because in recent games we have conceded late goals.
"We spoke about being motivated in the last 10 minutes and it was different as we were very strong and we scored goals."
Goodison Park has not been a happy home for them with fans quick to transfer their anxiety and anger onto the players on the pitch.
That is something the squad has had to learn to handle and Oviedo believes they are getting better at it.
"We have spoken about that," he added.
"We need to focus on ourselves and be clearer. Sometimes the fans want [us] to score goals but that is normal.
"At the moment we are just focusing on winning games and being nearer the top of the league as quickly as possible.
"We need to make a winning team. I think the team looked strong (against Newcastle) and we need to continue like that because the next games are very important for us."
Source: PA