Southampton are rock bottom of the league with 24 points and anything less than a victory against Fulham at home on Saturday will definitely see them relegated to the second-tier Championship with 17th-placed Everton on 32 points.
But Southampton have not won a game since they beat Leicester City in the first week of March, going on a 10-match winless run, and even victory over Fulham might just be delaying the inevitable with three rounds left.
"It's our job and our privilege to fight until the very last minute. It's not mathematically there, we are going to be there until the last moment," Selles told a press conference.
"It's getting harder (to motivate players) because the situation is not helping. It has been a difficult week for us."
Southampton have been in the top flight since they were last promoted in 2012 and Selles says the south-coast club can easily bounce back to return to the Premier League after one season.
"When a club gets relegated, it is a real issue for the city, the club, the players, the staff and workers. But the club has everything to bounce back straight away and be back the year after," he said.
"We have the support from a big city. We have a good structure with values and a philosophy."
However, Selles admitted it would be tough to retain most of the players with other Premier League clubs swooping in for their best talents.
When asked if he would love to continue managing the club in the Championship, the Spaniard said it was not up to him after he was appointed until the end of the season only.
"It's not been for me to decide but I would like to carry on (as manager) in the Championship and bounce back to the Premier League the year after," he said.
Fulham are 10th with nothing left to play for but Selles says he expects the London side to fight for their best-ever points finish in the Premier League.
"They have something to fight for, something to prove. They will be competitive, I expect the best version from them," he added.
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