Atletico, who are looking to secure a first Champions League semi-final spot in seven years, controlled the first half at the Metropolitano stadium and led 2-0 through Rodrigo De Paul and Samuel Lino.
But they had to soak up heavy pressure late on from Dortmund, who got a goal back through Sebastien Haller and then twice hit the woodwork.
"(We played) with a good pressure, we stole the ball, we forced the opposing team almost in the first half not to have goal situations in the game," Simeone told reporters.
"Now we'll go to their stadium knowing that we're going to find a strong team, a team with a lot of people who are going to take it to us, to attack. We will have to suffer and take advantage of the spaces.
"Seeing these first elimination ties, in the four (quarter-final) matches, it's not easy to win, so we're happy to have won."
Atletico next host Girona in the league on Saturday before travelling to Germany for the second leg against Dortmund on April 16.
