The Rojiblancos sporting director says the thought of reaching the final in Lisbon in May is a dream for the club and its fans, while president Enrique Cerezo lauded the Blues
Diego Simeone's men were drawn against Jose Mourinho's charges on Friday, with the first-leg taking place at the Vicente Calderon on April 22 before the return tie at Stamford Bridge eight days later.
Real Madrid or Bayern Munich await the victors, with the showpiece finale due to take place at Lisbon's Estadio da Luz on May 24.
In the immediate aftermath of the draw, Caminero was asked what he thought of the tie, with Chelsea possibly looking to avenge a 4-1 defeat in the Super Cup in 2012.
"This is totally different," he said. "I am happy to be among these three great teams.
"I think it's an even tie. We will follow the script of the team that wants to compete and fight.
"We'll try to be as consistent as possible with our style. We'll try to reach the final, which is a dream not only for the players but for the fans."
Club president Enrique Cerezo echoed the sentiments of Caminero: "We are going to face a great team. The semi-final will not be easy and is at 50 per cent.
"The two teams will fight hard and we will see a dramatic confrontation."
Atletico reached the semi-final stage by defeating Spanish rivals Barcelona, while Chelsea came from behind to knock out Paris Saint-Germain.