R. L. Bishop\ and\ B. O'Neill\ [Trans. Amer. Math. Soc. {\bf 145} (1969), 1--49; MR0251664 (40 \#4891)] introduced a class of warped product manifolds as follows: Let $(B, g_1)$ and $(F, g_2) $ be two Riemannian manifolds, $f\colon B \rightarrow (0,\infty) $ and $\pi\colon B \times F \rightarrow B$, $\eta\colon B \times F \rightarrow F$ the projection maps given by $\pi (p,q)=p$ and $\eta (p,q)=q$ for every $(p,q) \in B \times F.$ The warped product $M=B\times_f F$ is the manifold $B \times F$ equipped with the Riemannian structure such that $$ g(X,Y)=g_1(\pi_* X,\pi_* Y)+(f \circ \pi)^2 g_2(\eta_* X,\eta_* Y) $$ for every $X$ and $Y$ of $M$. The function $f$ is called the warping function of the warped product manifold. In particular, if the warping function is constant, then the manifold $M$ is said to be trivial. \par An odd-dimensional Riemannian manifold $(M, g)$ is called a contact metric manifold [D. E. Blair, {\it Riemannian geometry of contact and symplectic manifolds}, Progr. Math., 203, Birkhäuser Boston, Boston, MA, 2002; MR1874240 (2002m:53120)] if there exist a $(1, 1)$ tensor field $\phi$, a vector field $V$, called the characteristic vector field, and its $1$-form $\eta$ satisfying $$ \align g(\phi X,\phi Y) &= g(X,Y)- \eta(X)\eta(Y),\\ \phi^2(X) &= -X+\eta(X)V,\quad g(X,V)=\eta(X),\\ d\eta (X,Y) &= g(X,\phi Y),\quad \forall X, Y \in \Gamma(TM). \endalign $$ Then ($\phi,V,\eta, g$) is called the contact metric structure of $M$. We say that $M$ has a normal contact structure if $N_{\phi}+d\eta \otimes \xi=0$, where $N_{\phi}$ is the Nijenhuis tensor field of $\phi$. Let $\Phi$ be the fundamental 2-form on $M$ such that $\Phi(X, Y)=g(X, \phi Y)$. $M$ is called a locally conformal almost cosymplectic manifold if there exists a 1-form $\omega$ such that $d\Phi=2 \omega \wedge\Phi$, $d\eta=\omega\eta$ and $d\omega =0$. A locally conformal almost cosymplectic manifold $M$ ($\dim(M)\geq 5$) is of pointwise constant $\phi$ sectional curvature if and only if its curvature tensor $R$ is of the form $$ \align R(X, Y, Z, W)&=\frac{c-3f^2}{4}\{g(X, W)g(Y, Z)-g(X, Z)g(Y, W)\}\\ &+\frac{c+f^2}{4}\{g(X, \phi W)g(Y, \phi Z)-g(X, \phi Z)g(Y, \phi W)\\ &\hskip115pt-2g(X, \phi Y)g(Z, \phi W)\}\\ &+\left(\frac{c+f^2}{4}+f'\right)\{g(X, W)\eta(Y)\eta(Z)\\ &\hskip40pt-g(X, Z)\eta(Y)\eta(W)+g(Y,Z)\eta(X)\eta(W)\\ &\hskip124pt-g(Y,W)\eta(X)\eta(Z)\} \endalign $$ for $X, Y, Z, W$ vector fields on $M$, where $f$ is the function such that $\omega=f\eta$ and $f'=Vf$. \par On the other hand, B.-Y. Chen\ [Monatsh. Math. {\bf 133} (2001), no.~3, 177--195; MR1861136 (2002m:53082)] introduced CR-warped product submanifolds as follows: A submanifold $M$ of a Kähler manifold $\overline{M}$ is called a CR-warped product if it is the warped product $M_T \times_f M_{\perp}$ of a holomorphic submanifold $M_T$ and totally real submanifold $M_{\perp}$ of $\overline{M}.$ \par In this paper, the authors study $C$-totally real warped product submanifolds of locally conformal almost cosymplectic manifolds and establish the inequality between the warping function of a $C$-totally real warped product submanifold of a locally conformal almost cosymplectic manifold of pointwise constant $\phi$-sectional curvature and the squared mean curvature.