Palace visit Liverpool on Sunday before hosting Tottenham and then Burnley in the space of four days and Allardyce believes, if they can take their season's points total from 35 to 38, they can begin to plan for the 2017/18 season.
The manager has overseen an exceptional improvement since the end of the January transfer window, at which point the threat of relegation was significant.
However, despite Palace being so close to his target, he is not taking safety for granted or becoming over-ambitious.
"Thirty-eight points has been enough for (survival for) 10 years or more and we have got an opportunity to get there and get beyond it," said the 62-year-old.
"It is a big week for us to see how many points we can get. We want to take pressure off ourselves and get as many points as we can this week.
"At the end of this week there will only be three games left and, instead of one win out of six you might need one win out of three, which heaps the pressure back on again, so let's get as many points as we can.
"We are capable of getting points out of these games this week, as we have proved in the last six or seven games. I hope the players believe, as I believe, that they are capable of getting points out of them.
"Taking five wins out of six - and six wins out of nine - and we are still not safe, so it shows just how difficult a task it was to get us out of the bottom three."
Read the full article on eurosport.co.uk: One more win will see us safe, says Palace boss Allardyce