Barca went down 2-0 at the San Siro in the first leg of their last-16 tie with the Italians.
"It's a really bad result," Pique told UEFA's official website. "We played badly and can't make excuses.
"We will obviously try to win the return game. We must improve and learn from tonight. We will look to respond on one of those magical nights at the Camp Nou."
Pique and his teammates welcome Milan to the Camp Nou for the second leg on March 12.