The Red Devils were on the verge of suffering a 1-0 defeat against the Russians before new signing Anthony Martial popped with an equaliser in the 65th minute of the tie.
The draw at the Arena Khimki leaves United in second spot in Group B, which is currently topped by German giants Wolfsburg.
Schweinsteiger, as well as his team-mates, was disappointed with the draw in Russia and has told fans the team will endeavour to get a positive result next time they face Leonid Slutsky's side.
"Unfortunately, no win yesterday, he wrote in a post on Instagram.
Unfortunately, no win yesterday. As expected, Moscow required everything from us. In two weeks at Old Trafford we’ll have the chance to put us in a better position. #mufc Leider kein Sieg gestern. Wie erwartet, hat uns Moskau alles abverlangt. In zwei Wochen haben wir aber im Old Trafford die Möglichkeit, unsere Ausgangslage in der Gruppe zu verbessern.
"As expected, Moscow required everything from us.
"In two weeks at Old Trafford we’ll have the chance to put us in a better position."
