Costa's Atletico progressed to the European final with a 3-1 second leg, and aggregate, victory over Jose Mourinho's Blues, with the star striker putting the La Liga leaders ahead with a penalty on the hour-mark.
Leading up to his spot-kick, Costa was cautioned for roughing up the penalty spot, but he claimed he could not get the ball to sit properly on it, before converting past Blues goalkeeper Mark Schwarzer.
"The ball kept leaning forward and I wanted it to be level, but it went well," Costa said.
Atletico trailed after 36 minutes, when former striker Fernando Torres tucked away the opening goal, but Costa did not panic - with the knowledge an away goal would put them in front.
He also confirmed his substitution on 76 minutes was not due to any serious injury.
"Torres scored the goal but we knew that ours would be worth two and we had to fight for it," Costa said.
"The injury is just a knock, that's all.
"The final against (Real) Madrid? We'll be there and ready."
Costa failed to rule out a switch to Chelsea, with rumours swirling the London club are looming for his services.
"Chelsea in my future? We'll see, I know there are offers for me. I feel well here at Atletico. Let's see," he said.
Midfielder Koke said he had to erase thoughts of the final from his mind, despite knowing a yellow card in the second leg would have suspended him from the Lisbon showpiece.
"I tried not to think about the final," Koke said.
"I was fortunate enough not to get booked, but if I’d had to stick my foot in for a challenge, I would have done without hesitation.
"All I was thinking about, was helping Atletico get through to the final."
Koke praised boss Diego Simeone for his message, despite not being able to clearly hear the Argentine throughout the second leg.
"It was almost impossible to hear him. Simeone is happy with my work though," he said.
"The manager hasn't filled our heads with anything unnecessary, because going out there to win the game, was motivation enough."
