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."
Middlesbrough have hit a dip in form and have slipped out of the npower Championship play-off places having only won one of their last nine league games.
Tony Mowbray's side has several injury concerns ahead of their FA Cup match with the reigning European champions.
Jonathan Woodgate (calf) and Seb Hines (knee) are both doubtful for the match while Stuart Parnaby (hamstring) and Justin Hoyte (hip) are both ruled out.
Meanwhile, Everton midfielder Darron Gibson is keen to make amends after last season's FA Cup campaign saw his side beaten by arch-rivals Liverpool at the semi-final stage.
A fifth-round replay against Oldham stands in the way of David Moyes' Toffees progressing into the quarter-finals of the competition.
Gibson was part of the squad who made it to the last four only to be beaten 2-1 by Liverpool and he is keeping that result in mind as motivation when the Premier League side host npower League One's Oldham.
"I love playing at Wembley," Gibson told evertontv. "Obviously last season it was great getting there but it was disappointing to lose.
"We started the game really well, went 1-0 up but maybe froze a little bit. Hopefully we can get back there this year and make it right.
"Having it (the route to Wembley) laid out in front of us does make it a bit easier because we know if we play well enough we can beat Oldham.
"Then, if we make it to the next round, we know Wigan are a good team but we have played them at home already this season and beaten them."
Everton's rematch with Oldham comes after the sides drew 2-2 at Boundary Park earlier this month and Oldham's on-loan winger Jordan Obita is hoping for a goalscoring return.
The 19-year-old winger, who is on loan from Reading, gave the Latics the lead in that fixture before Victor Anichebe and Phil Jagielka put Everton in front, only for Matt Smith's last-gasp equaliser to ensure a replay.
"As a player, you want to play against the best. I thought every one of our players did well against Premier League footballers," Obita told the club's official website.
"The last time (I played at Goodison Park) was in a reserve-team match for Reading, but tomorrow [Tuesday] will be far different with a big crowd to cheer us on.
"Hopefully our fans can help us win the game. It is a nice stadium and the pitch is amazing."
Tuesday's FA Cup Fixture
Everton vs Oldham
Wednesday's FA Cup Fixture
Middlesbrough vs Chelsea