Histon strengthened their play-off hopes but Wrexham's all but ended after this stalemate at the Racecourse.
Ashley Westwood saw a header for the home side cleared off the line just before the break.
Then Andrew Crofts sent a left-foot shot towards the top corner, but Histon keeper Danny Naisbitt turned it around the post.
The visitors' best chance fell to Jack Midson and Gunnar Nielson had to palm his hooked shot away.
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Wrexham manager Dean Saunders:
"Determination-wise, they all did really well. It was one of those games you wish you had stayed in the house to watch.
"Going forward, they stopped us from playing any football whatsoever.
"We needed a win tonight. I think it's [play-offs] going to be very difficult now."
Wrexham: Neilsen, Westwood, Collin, Assoumani, Mike Williams, Spann (Baynes 64), Fleming, Crofts, Taylor (Williamson 70), Louis, Brown (Flynn 74). Subs Not Used: Suffo, Fairhurst.
Histon: Naisbitt, Oyebanjo, Langston, Ada, Gwillim, Murray, Mitchell-King, Simpson, Knight-Percival, Midson, Wright. Subs Not Used: Welch, Pope, Bygrave, Roache, Barker.
Booked: Ada, Mitchell-King.
Att: 2,234
Ref: Paul Tierney (Wigan).
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