Milan were held 1-1 on Sunday.
"It was a tough match but we played a good game," Essien told Milan Channel.
"We also had the chance to win, but unfortunately we did not succeed. At San Siro it was a great atmosphere.
"There were some good moves from the team, I was very happy for the goal Menez scored.
"El Shaarawy had a great chance to win the derby for us, but now we must only think of the next match."
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