With 38 points they should just about avoid being dragged into the scrap for survival over their final half-dozen games.
However, Allardyce said: "With all the bottom sides seeming to be picking up more points now than they have done for the rest of the season, I would say we are still another couple of points off being absolutely safe."
The Irons, though, also remain within striking distance of the top half, which would represent a remarkable achievement from Allardyce's squad on a first season back in the top flight.
"We have got four home games and two away, so we have an opportunity (to get into the top 10), but I think we are going to have to win three and draw two out of the last six," he said.
"In fact they will all be tough, even Wigan who are now in a position, because of being in the FA Cup final, that they have games to catch up and points to gain on others.
"That puts the pressure on them, so they will all be really tough matches but hopefully we can win a couple and see where we go."