The England international had a great opportunity to salvage a point for his side after they hit the front but then fell behind 2-1 to City but his spot-kick was well-saved by opposing keeper Shay Given and the Blues left Manchester with nothing.
Essien says Lampard is mentally strong enough to deal with his miss and is already looking to atone for it.
"Frank is a very strong guy, very strong mentally," Essien said.
"These things happen. Anyone can miss a penalty. He's not the first and he won't be the last. He's put it behind him and is looking to the future. He's our best penalty taker at this club."