Roberto Martinez's side are currently 11th in the table after 19 games.
The Blues are currently 11th in the table on 26 points with half of the season gone, nine points from Tottenham who currently occupy fourth place.
It has been a highly frustrating period for Roberto Martinez’s side recently, with them playing well but failing to secure all three points in a number of games.
The unpredictable nature of the Premier League this season means that any number of sides could make the top four this season however, and Lukaku believes Everton can be among those challenging.
“I think the way the league is going, a lot of things can happen,” he told Sky Sports.
"If we get a few wins on the bounce and get momentum then we can end the season well, but it's up to us.”
"We need to win games and make sure if we are in good situations we manage the games well, that's something we need to work on and as soon as we do it we will be going up in the league."
If Everton are to start climbing back up the table and compete for a place in Europe, it is the defence that will need resolving above anything.
The Blues have been in fine goal scoring form so far, with Lukaku currently the joint top goalscorer in the Premier League alongside Jamie Vardy.
Defensively though, they have been poor, conceding 28 goals already and a whopping seven in their last two home games alone.
That is clearly their Achilles heal then, and something they must seek to solve quickly if they want a place higher up the table.