Simeone: No excuses for Atletico slip-up
Simeone's men failed to take their chance to stay three points clear atop La Liga with the surprise loss to a team sitting 13th.
Verza struck twice in the final 10 minutes for Almeria at the Estadio de los Juegos Mediterraneos, including the second from the penalty spot after Atletico goalkeeper Daniel Aranzubia saw red.
Simeone was unwilling to complain about his team's busy run of tough matches or the controversial red card to Aranzubia.
"The opponent tried to play their game. In the first half we could have done better, we created some chances, but football has these things, sometimes you win, some are tied and you lose some," the Argentine said.
"We do not seek excuses, we will not blame the referee, or the wind, or the ball.
"The opponent did a great job and congratulations on that. The only way we know to follow this line is working, and we will."
Atletico had faced Real Madrid in the Copa del Rey and European-chasing duo Real Sociedad and Athletic Bilbao before the Almeria clash.
But Simeone said fatigue – mental or physical – was no excuse for his team against Almeria.
"I do not think that it is related, at all times the team came out to take the game in the way they could," he said.
Simeone was unwilling to comment on the Aranzubia penalty, saying he was yet to see a replay of the incident.
The goalkeeper was adjudged to have brought down Jonathan Zongo near the goal-line, giving away a penalty and being sent off despite appearing to make very little contact.
Simeone said he was more concerned about midfielder Tiago, who was substituted after a dreadful lunge by Helder Barbosa – which went unpunished.