Saturday's 1-0 defeat at Stoke leaves Rovers just three points clear of the drop zone with games against Wigan, Manchester City, Portsmouth, Chelsea and West Brom still to come.
"It is a difficult situation to be in but we are outside of the bottom three and are in the best position we have been since I took over," said Allardyce.
"When I took over we had 13 points from 17 games and we have had a long, hard battle to get where we have got now and we are still three very valuable points off that bottom three.
"Making sure we don't lose another game is key to us now. With five games left, if we don't lose I think we will be okay.
"But we have to try to get a win as early as we can and if we can't win make sure we don't lose.
"There is only Chelsea that is difficult for us, all the other games I think we can get something out of.
"We have three very important home games, Wigan, Portsmouth and West Brom (on the final day of the season) but we don't want to go to the last game, we want to secure our Premier League status as soon as possible."