Missed Defence

It must have been time trouble that Black missed a strong defence in the diagram below from Nisipeanu - Tregubov (Aix-les-Bains 2011).

With his last move 39.Qf2-b2? White threw away the win, but Black didn't notice it and played 39.- Rxe3? and then resigned after 40.Qb8.

Instead 39.- f4! would have made the draw with the perpetual check Qg3+/Qe1+. What a pity!