Memphis Depay’s 37th-minute opener was cancelled out by Pione Sisto before Paul Onuachu secured a famous win for the home side in freezing conditions.
United have lost their last two games in all competitions ahead of Monday night’s trip to League One side Shrewsbury Town in the FA Cup fifth round.
Former Republic of Ireland international Giles was talking on Irish radio when he learned of United’s latest nadir, and the retired midfielder couldn’t hide his shock.
When told of the result, Giles replied: “Oh god.”
United host the Danish champions in the second leg of their Europa League clash next Thursday evening at Old Trafford.
The 20-time English champions will face Arsenal in their next Premier League game at Old Trafford on Sunday 28 February.
United are in fifth place in the Premier League table.
Get 8/1 enhanced odds on Tottenham to win or 11/1 enhanced odds on Liverpool to win at White Hart Lane on Saturday afternoon. Click here to sign up now. T&Cs apply.
MORE: Latest Man Utd news
MORE: Latest Arsenal news
MORE: The latest football news