Uruguayan defender Diego Godin's goal shortly before half-time ensured Madrid a vital advantage in the quarter-final tie.
Simeone was surprised with the free-flowing style that the game was played in and maintained little split the two teams going into the second leg.
"This was a classic cup game, that is competitive, in which the two teams play for a positive result," Simeone said.
"A 2-0 loss would not have suited Bilbao but a 1-1 draw would so they went for it.
"We didn't expect to see a very open game, perhaps we thought it would be more open in the second one with the result to play for, but not in the first cup games.
"From the experiences I've had, the first legs are always much more studied, but I don't think that was the way tonight."
The Argentine tactician said Wednesday's second leg in Bilbao will be a difficult encounter and after his Madrid side play away in the league at Rayo Vallecano on Sunday, he will ensure his players are prepared to progress to the semi-finals of the cup competition.
"After Sunday night, we will prepare for the game in the best way because it will be a tough match in a beautiful environment to play football with a team that is strong," Simeone said.
"Bilbao is having a very good season so far, they are fourth in the league and playing good football.
"To keep that place in the league would be exhausting, so we must be attentive and make sure we are focused.
"We have to be aware of what they need to do."
