Andersen scored in the first-half as the Eagles went 2-0 up, but City came back in the second-half to score four times and take the three points.
Andersen said: "We scored two set-pieces in the first-half - that was the difference [between the two halves].
"I feel like we waited a little bit too much on them today, and then we became more tired in the second half. They scored an early goal and then you know it's going to be tough against City because they have so much quality.
"It's Manchester City away - it's always a tough game, and all credit to them."
Asked if he felt his side had scored their first-half goals too early, Andersen said: "No.
"But sometimes when you get in front then you sit back a little bit more.
"We shouldn't have done that.
"We should have been more in their face and more aggressive in the press.
"When you give them so much time on the ball they will always find the space.
"They have so much movement up there and I feel like we were not aggressive enough when we were sitting back."
Andersen expanded on the challenge playing a side like City poses, when they begin to find their groove.
"It's really, really hard," the Dane said.
"Last season we didn't concede against them, it was a bit similar games but we had that little luck so they didn't score when they had big chances.
"And today we didn't [have that luck], that's football sometimes.
"It's so difficult to play against City, because you need to expect the unexpected, they will find that little metre of space."