The statement is false. For example, for the case of $d=1$, it is known that the largest number of consecutive quadratic residues modulo $p$ tends to infinity as $p\to\infty$. See [here][1] and, for more general patterns, see Seva's answer to [this MO question][2]. Further related MO entries are [here][3] and [here][4].

**Added.** Seva's answer (linked above) shows that the statement is false for every $d$.


  [1]: https://math.stackexchange.com/questions/716182/consecutive-quadratic-residues
  [2]: http://mathoverflow.net/questions/161271/consecutive-non-quadratic-residues
  [3]: http://mathoverflow.net/questions/146258/quadratic-residues-and-nonresidues-of-arbitrary-patterns
  [4]: http://mathoverflow.net/questions/85842/three-consecutive-quadratic-residues-problem