In a week where Chelsea booked their place in the last 16 of the Europa League, the 2-0 loss at the Etihad left them 19 points adrift of league leaders Manchester United and seven behind City.
However, Mata has urged fans to remain positive as Chelsea are still in the mix for two trophies, with Wednesday's match against Boro their chance to move into the quarter-finals of the FA Cup.
"We're sorry for our fans," Mata told the club's official website.
"The way to overcome the disappointment is winning again, and this coming Wednesday we have an opportunity to move one step forward in the FA Cup.
"We can still win two titles. That, plus getting a ticket to play the next Champions League, is our motivation with a view to the rest of the season and we will fight for those goals until the end, like this club has always done."