The coach did not blame los Rojiblancos' slip-up on the Copa del Rey clash played just days earlier
Verza's double, courtesy of a pair of Dani Aranzubia errors, condemned the title contenders to their second defeat this week following Wednesday's 3-0 loss to Real Madrid in the Copa del Rey.
But Simeone denied that his men were exhausted by the derby clash and refrained from blaming windy conditions or the referee for a controversial penalty awarded to the hosts.
"Almeria played as they planned to. We had our own chances. Football is like this. We won't look for excuses. Well done to Almeria," the Argentine boss told reporters after the match.
"I don't think we were tired [following the Copa game versus Madrid]. We were prepared for this game. We won't blame the referee, the wind or anything."
Midfielder Tiago could face a spell on the sidelines following a rugged challenge from Helder Barbosa and Simeone admitted his concern: "The thing I'm most worried about today is Tiago."
The extent of the Portuguese's injury is unknown, but he could be out of the Copa return leg clash versus Madrid as well as the Champions League tie with AC Milan.
Local rivals Madrid are now level on 57 points and sees them move to first in La Liga. Barcelona travel to Sevilla on Sunday.