I agree with Binoy Bera. There are several factors to describe the perovskite materials are not a piezoelectric such as crystal structure (symmetry as well) and microstructure (grain size). In my work, I found a tetragonal phase in perovskites materials but not they are not piezoelectric materials because the grain sizes are too small which it does not have 90 domain walls.
You can check the point group of the crystal to determine it it is piezoelectric. There are 32 point group symmetry and 21 of them are piezoelectric. Therefore, there are several crystal that are tetragona/orthorhombic/monoclinic/rombohedral, but they are centro-symmetric and non-piezoelectric. Example: CaTiO3 at room temperature and atmospheric pressure.
As mentioned by other researchers piezoelectric materials do not show piezoelectric effect if
(1) They posses centre of symmetry,
(2) At room temperature they show paraelectric phase.
(3) They have very high coercive field (Hard) and difficult to demonstrate piezo effect at normal conditions
(4) Lack of 90 degree domain wall as suggested by Mr. Piyaporn Jaimeewong. In this case, only 180 degree domain switching, which is responsible for most of the polarization can be observed.
Check the article
T. Tsurumi, Y. Kumano, N. Ohashi, O. Fukunaga 90o Domain reorientation and electric-field-induced strain of tetragonal lead zirconate titanate ceramics, Jpn. J. Appl. Phys., 36 (1997) 5970.
B. A. Tuttle, T. J. Garino, J. A. Voigt, T. J. Headley, D. Dimos, M. O. Eatough, Relationships between ferroelectric 90 domain formation and electrical properties of chemically prepared Pb(Zr,Ti)O3 thin films, Science and Technology of Electroceramic Thin Films, ed. O. Auciello and R. Waser (Dordrecht: Kluwer) (1995) p 117.