United performed well at times against what was a rotated and relatively open Gunners side, but few inside Old Trafford could have reasonably argued had the visitors sneaked a win.
There were a handful of positives for United going forward. Anthony Martial scored his seventh Premier League of the season, while Jesse Lingard found the net in a United shirt for the first time since February. The nature of the comeback was also good after twice going behind.
Despite being part of a defensive unit that leaked two more goals, Eric Bailly also impressed, offering significant promise and hope for the coming months.
Both Arsenal goals were the result of avoidable individual errors - first from David de Gea and later from Marcos Rojo. Bailly was not at fault in these moments and the Ivorian seemed desperate to prove himself on what was his first appearance in two months.
In difficult circumstances, United fans could have asked little more of Bailly. He was aggressive and hungry in his attempts to win the ball, often stepping up into midfield to make tackles on the front foot or win headers. He even tried to set off attacks by driving forward with the ball. That is not his game and likely never will be, but it was a positive show of willingness nevertheless.
Bailly was so out of favour with Mourinho, a manager who seems to work off trust above all else as far as his defenders are concerned, that he went five straight Premier League without even being named in the matchday squad between late October and early December.
When the 24-year-old finally stepped back onto the Old Trafford pitch against Arsenal he was clearly very eager to make the most of it now that his opportunity had at last come back around.
Still quite raw, Bailly has all the physical attributes needed to thrive in the Premier League and is still young enough that he can become a genuinely world class centre-back once his rough edges have been smoothed and his occasional rashness tempered.
It is worth remembering that ex-United captain Nemanja Vidic, a player with whose aggressive style it is possible to draw comparisons to Bailly, was older at 25 years of age when he arrived in Manchester in January 2006 and still wasn't the finished article until a year or two later.
Time is on Bailly's side if those in charge will afford it to him, and this week's game at least showed the player is still heading in the right direction.