Roberto Martinez's side sit fifth in the Premier League table having only succumbed to defeat once all season - a 3-1 defeat to Manchester City.
The Toffees have enjoyed victories over Chelsea and Manchester United this term, before securing a hard-fought point against Arsenal last weekend and the Irishman is daring to dream of a top-four finish in May.
Speaking to the Daily Mail, the defender said: "It has been a big couple of weeks. We knew it was going to be tough at Old Trafford but the manager told us if we could get positive results, it would set us up nicely.
"We then went to the Emirates wanting to win. Even when Arsenal scored, we never felt dead and buried.
"There are a lot of teams who are up fighting with us but we have faith in what we can do. It would be a dream to finish in the top four."
The Republic of Ireland full-back has netted twice in 22 appearances for the Liverpool-based outfit this season.
Everton host Fulham at Goodison Park this afternoon from 3pm.