The division’s bottom club sit six points adrift of safety ahead of Sunday afternoon’s challenging visit to St James’ Park.
Saints manager Selles acknowledges time is running out and wants his players to be brave as they bid to secure a shock result and keep alive their slim survival hopes.
“I think we have been talking about that in the last five to six games,” the Spaniard said of must-win fixtures.
“Of course it’s a game that we must win and every game has become a game that we must win, more now than ever.
“And that’s what we’re going to try, we’re going to try to go for it.
“I will keep my positivity until the very end. I still think we can do it and I still think everybody in the club is able to do it.
“We just need to keep that belief because then things can change.”
Southampton are on an alarming eight-match winless run following Thursday’s meek 1-0 loss to Bournemouth, which was a club-record 11th home defeat of the season.
Meanwhile, third-placed Newcastle have been in freescoring form as they close in on a return to European football’s premier competition for the first time in 20 years.
Selles believes victory at Chelsea in his first match in charge and draws against Tottenham, Manchester United and leaders Arsenal demonstrates his under-performing players are capable of upsetting the odds.
“I think they have proved that they are good enough to win games in the Premier League and then we have made some good performances against the top teams,” he said.
“That should be the boost we need to use for the next game. We need to go against one of the top teams again and everybody should be ready for the challenge.
“It’s not an easy situation. We need to be on point for that game.”