The Red Devils managed to score a crucial away goal through Henrikh Mkhitaryan in the opening half at the Stadion Olimp-2 before Alexander Bukharov responded for the Russians with a well-taken second-half equaliser.
On a night where the subpar playing surface hindered the quality of the contest, Mourinho felt it was a satisfying result for his side who will return to Old Trafford to host Rostov next Thursday.
"It was a very good performance in relation to the conditions," he told BT Sport.
"Impossible to play better, impossible to have the ball, impossible to play a passing game. We played what the game demanded from us, we played well.
"We made one defensive mistake, but we can't concede a goal like that. We cope with the intensity, with their direct game, and the result is what we could expect.
"An open result for the second leg with a little advantage for us.
"It was a difficult match and now Old Trafford."