We investigate the influence of efficacy of synaptic interaction on firing synchronization in excitatory neuronal networks. We find spike death phenomena: namely, the state of neurons transits from the limit cycle to a fixed point or transient state. The phenomena occur under the perturbation of an excitatory synaptic interaction, which has a high efficacy. We show that the decrease of synaptic current results in spike death through depressing the feedback of the sodium ionic current. In the networks with the spike death property the degree of synchronization is lower and insensitive to the heterogeneity of neurons. The mechanism of the influence is that the transition of the neuron state disrupts the adjustment of the rhythm of the neurons oscillation and prevents a further increase of the firing synchronization.