Steve Melton had the best chance early on, but shot just wide after moving into the box.
Wrexham had by far the better of the possession, but failed to create many clear cut opportunities. Lee Trundle had three shots on goal, while John Anderson almost headed into his own net, but City held on until the break.
Paul Musselwhite denied Andy Morrell in the opening minute of the second half, and then blocked Trundle's effort from the resulting corner.
Sloppy defending from Damien Delaney allowed Trundle to take the ball off him, and as he attempted to set up Darren Ferguson, Ian Ashbee managed to make a fantastic tackle to save Delaney's blushes.
Stuart Green had City's only real opportunity of the second half, but Whitfield saved his low effort.
Phil Jevons was brought on soon later, and Marc Joseph also came on to make his City debut, but neither made any difference to the scoreline as it finished 0-0.
City line-up (4-4-2): Musselwhite; Regan, Whittle, Anderson, Delaney; Green, Melton, Ashbee, Keates; Alexander (Jevons 61), Branch (Joseph 80).
Un-used subs: Deeney, Smith, Elliott.