After a disappointing 3-1 loss to West Ham United in Saturday's Premier League fixture, Jose Mourinho's men put in a decent shift against the Spanish side but struggled to break the deadlock.
The result meant they are without a win across all competitions since their 3-0 victory over Young Boys in their Champions League opener on September 19.
Manchester United have now failed to win their last four home games but the Ivorian, who played alongside Chris Smalling in centre-back on Tuesday, admitted that they were close to securing maximum points in front of their home fans.
"Victory was close tonight, but this is the way forward," Bailly wrote on Instagram.
Bailly made his fourth start for the Red Devils this season and was on parade for the entire duration.
Having garnered four points from two games, United are placed second behind Juventus who maintained a 100 percent win record in the elite European competition this campaign.
Next up for Jose Mourinho's men is a Premier League meeting against Newcastle United at the Old Trafford on Saturday.