Dowie was banking on an impressive haul from his team's home games in the run-in, but they have taken only one point from the last two matches at Selhurst Park.
Palace have also not won sinc e February and have just five games to haul themselves out of the bottom three.
A few weeks ago Dowie would probably have described a draw at Blackburn on Wednesday as being a good result but that is no longer the case.
He said: "We will take the point against Norwich, but we have got to go to Blackburn and get more than that.
"Saturday's result kept a good cushion between us and Norwich. The heart and spirit of the lads was brilliant and we need to take that into our next game."
It is rare for a team in the relegation places at this stage of a Premiership season to escape and the players are aware they cannot afford to slip up again.
But after their unlikely promotion last season, they believe anything is possible.
Mikele Leigertwood said: "I have not seen it in the dressing room, but probably quietly the players are looking at the fixtures and doing the maths.
"The last two home games against Norwich and Middlesbrough were missed opportunities, but Iain has told us to stay positive and keep going.
"Last year we lost to Coventry on the last day of the season, but West Ham stoppedWigan winning to put us in the play-offs. Our luck might change again this season. We need to get back to basics and do what we are good at."