Although CSKA dropped into the Europa League after Basel beat Benfica to join United in the last 16, the Russian side's manager Viktor Goncharenko said the Champions League campaign would serve his players well.
The victory guaranteed Mourinho's side top spot in Group A of the Champions League.
United were always likely to finish top of the group even if CSKA had won the match, such was their strong advantage in the head-to-head reckoning, but Mata was pleased they came back to win ahead of Sunday's Premier League clash with Manchester City.
Meanwhile, midfield is seen as a priority as well with Marouane Fellaini, Ander Herrera and Michael Carrick in their final year and they need a stable replacement for the latter to say at the most.
The 35-year-old, who now plies his trade with Persib Bandung in Indonesia, opted to support Jose Mourinho's side even while his former club Chelsea played against Atletico Madrid at the same time at Stamford Bridge.
Mourinho joked Arsenal's medical team had performed an "amazing" feat by turning Lacazette "from a no to a complete 90 minutes".
Mourinho was also delighted with the performance with Luke Shaw and Sergio Romero. "Sunday is a big game; we know how important it is".
Vietnam Veterans pay respects on the 76th anniversary of Pearl Harbor
The United States was particularly unhappy with Japan's increasingly belligerent attitude toward China. He told the story of an officer who warned friends of the impending attack, only to be ignored.
"Discussing Shaw's display, Mourinho told Sky Sports: "[It was a] very, very positive performance, especially with the ball going forward.
"Really unsafe, creating a lot, great intensity in his game".
The Chelsea-Atletico match in England still had a couple of more minutes to go after the final whistle in Rome.
Dzagoev appeared to be in an offside position, but the goal was allowed to stand - credited to Vitinho - because Daley Blind was adjudged to have played him onside despite having slid off the pitch.
Second half strikes from Romelu Lukaku and Marcus Rashford cancelled out Alan Dzagoev's opener for CSKA Moscow. In battles against Arsene Wenger's Arsenal, the teams were usually well-matched in terms of stars - Dennis Bergkamp for Eric Cantona, Patrick Vieira for Roy Keane, Tony Adams for Jaap Stam - and, at both sides' best, Arsenal played better football. Bayern Munich, Juventus, Sevilla, Shakhtar Donetsk, Porto, Real Madrid. will all be on the cards when the group 16 drawing takes place December 11.
"Considering we finished third in the group, it's not a bad result, and fighting for qualification until the last day is not bad either", he said.
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