The Argentine was given his marching orders just 26 minutes in following another trademark altercation with officials on the touchline.
By that point Mario Mandzukic had put his side 1-0 in front on the night and 2-1 ahead on aggregate, after just two minutes.
That goal proved enough to clinch the trophy and Simeone was quick to say sorry for his actions following the game, blaming his behaviour on the emotions of the night.
He said: "It was the anxiety, nerves. I can only apologise."
The result will give Atletico momentum as they prepare to begin their La Liga defence against Rayo Vallecano on August 25, with Simeone admitting the victory has come as a timely boost.
"I am delighted with the work of these boys," he added.
"We have faced a great champion like Madrid twice and to beat a great opponent like this gives us great energy and motivation moving forwards."