In contrast with the subcritical case, we prove that for any bounded domain $\Omega$ in $\mathbb{R}^3$, the Neumann elliptic problem with critical nonlinearity $-\Delta u + \mu u = u^{5}$, $u > 0$ in $\Omega$, $\partial u / \partial n= 0$ on $\partial\Omega$ has no solution blowing up at only interior points as μ goes to infinity.