United suffered their first Premier League defeat at home since City's last visit in September 2016, with Jose Mourinho's side beaten 2-1 on Sunday.
Goals from David Silva and Nicolas Otamendi secured all three points for City, a record 14th successive win in a single top-flight campaign, giving them an 11-point lead at the summit.
Despite the "painful" defeat, Mata says it is important United bounce back with games against Bournemouth and West Brom in the coming week.
Writing in his personal blog, Mata said: "Unfortunately, we couldn't finish the week as we expected since the derby at Old Trafford didn't work out as we wanted.
"City took the lead, we tied the score before the break but, in the second half, we couldn't overcome their second goal. We were close, but in the chances we had, the ball just didn't go in.
"The truth is these are three points like in any other game, although the defeat is painful because it was a derby. We must carry on, knowing that there's still a long way to go.
"The calendar gives you no time for mourning and we have to focus on what's next.
"The list of fixtures is very demanding this month so it's important to get to each game in the best condition possible.
"I think we have the ability to do it, even though we know these are the toughest weeks of the season. We are Manchester United and we have experience in playing every few days."