United will now head back to England with a vital away goal in their grasp ahead of the second leg at Old Trafford next Thursday.
Winning the Europa League also comes with the bonus of Champions League qualification but Mourinho said his priority was for United to finish as high up in the Premier League table as possible.
"The Europa League is very hard but it's a target for us", he told British media.
"In the Europa League, if we manage to go through this knock-out round, we go to the quarter-final and then you feel that the door is open".
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Rashford was thrust from the academy and started 18 of United's final 19 games last season, scoring eight goals.
"I don't know which team I will play, I don't know if Mkhitaryan is going to play", he added.
Mourinho plumped for a three-man defence after stewing on his team selection overnight once he had seen the state of the Olimp-2 surface first-hand.
United won the European Cup in 1968, the Cup Winners' Cup in 1991 and Champions League in 1999 and 2008. They can not afford to underestimate Rostov who beat Anderlecht and Ajax in the Champions League qualifiers to be drawn alongside Bayern Munich and Atletico Madrid in the group stage of the competition.
United is vying with Arsenal, Liverpool, Manchester City and Tottenham for a top-four spot, with Chelsea looking to have secured the Premier League title with a 10-point lead.
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Jose Mourinho has named a 20-man squad for the game, but has also omitted Luke Shaw and Bastian Schweinsteiger.
"I don't want to speak about the pitch because for both sides the pitch was an very bad thing".
Jose Mourinho and his men will be really confident ahead of this match given that Rostov have never faced an English team before, but the bigger concern prior to this match was the condition of the pitch. Hopefully, we will come into this match on top, both physically and mentally.
Fast forward 12 months and Rashford has drifted out of the spotlight, and is mainly found either on United's substitutes' bench or pushed out to the wing to accommodate the new striker sensation at Old Trafford, Zlatan Ibrahimovic.
Rostov will likely be at full-strength except for doubts over injured first-choice goalkeeper Soslan Dzhanayev.
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