The Liga leaders could complete an historic double of domestic and European titles, after they downed Chelsea 3-1 in London on Wednesday to oust Jose Mourinho's men from the competition.
Chelsea had taken the upper-hand, earning a scoreless draw in the first leg in Spain before striking first at Stamford Bridge through former Atletico captain Fernando Torres.
But the Blues' defensive structures - the centre of much criticism of late - crumbled as Adrian Lopez, Diego Costa and Arda Turan all scored to continue Atletico's stunning season.
Tiago, a former Chelsea player, said his side simply had to believe they could score away from home.
"It's a dream. We have a great spirit and a great team and we all work together. Now we go to the final in Lisbon and the dreams can become true," Tiago told Sky Sports.
"It's not easy to play at Stamford Bridge but we knew that Chelsea had to play more and score a goal.
"We had confidence because we know we are very good playing away. We scored and after our goal I think Chelsea were a bit down and we became more confident.
"It was very important to go into half-time at 1-1. That's the way we like to play - in that moment we knew Chelsea had to play more in the second half."
Tiago said Atletico felt their defence would not be breached more than once, and it was stability at the back that saw the visitors comfortably through - as Chelsea required three goals to advance after they went 3-1 down in the 72nd minute.
"Our belief was the key to success. We knew, if we scored one goal, we would do it. This did not change after Chelsea had scored," he said.
"In the end it was a deserved victory. Especially in the second half we were able to press Chelsea into their own half.
"We will enjoy this moment as much as we can. I am very proud of this team and of our superb fans."
