Roberto Martinez believes Everton will overhaul Arsenal into the race to qualify for the Champions League if they win their last three matches.
Martinez’s fifth-placed team trail fourth-placed Arsenal by a point after their bid to finish in the top four fell out of their own hands with last week’s 3-2 defeat at Crystal Palace.
A 2-0 win over Manchester United on Sunday in the following match revived Everton’s belief they can still qualify for Europe’s elite club competition.
Now Everton head to Southampton on Saturday before hosting Manchester City and then finishing the Premier League season at Hull.
The Gunners end their campaign with matches against Newcastle, West Brom and Norwich, making them favourites to win the qualification battle.
But Martinez remains confident three more victories will be enough to overtake Arsene Wenger’s team.
“Looking at the last 15 years or so, fourth place is well below 76 points,” Martinez said.
“There has only been one season where you have needed 76 points for that (fourth) and on average it’s always been a lot less points.
“You don’t go far wrong when you look at the points tally. We are well aware anything around 72 to 75 points is Champions League football so we are desperate to try to make sure we get that.”
However, Martinez’s hopes for a Champions League spot are in danger of being hampered by Everton’s long injury list.
Belgium winger Kevin Mirallas has been ruled out for the season with a groin problem, while defender Sylvain Distin is out of the trip to Southampton with a hamstring injury.
Captain Phil Jagielka is still sidelined, along with Bryan Oviedo, Darron Gibson, Steven Pienaar, Lacina Traore and Arouna Kone.
Southampton have little to play for except to hold on to eighth place, which would equal their previous best Premier League finish in 2003.
However, a number of players have a great deal more on their personal horizons as Adam Lallana, Rickie Lambert and Luke Shaw are all keen to be included in the England World Cup squad as soon as the season is concluded.