After taking the lead through Anthony Martial, United trailed at the interval from goals by Naldo and Vieirinha but, in a contest of huge momentum swings, the visitors were poised to advance from a losing position when CSKA Moscow took the lead at PSV Eindhoven.
However, the game swung once and for all in a dramatic 60-second period which started when United took an 82nd minute lead as Marouane Fellaini jumped high to meet a Daley Blind corner and forced Joshua Guilavogui into conceding an own goal as the ball flew in off his head.
With the game level, and PSV drawing in the other match, United were still in second place in the pool and on course for a place in the last 16 and the potential €69m riches awaiting them there. It was a dream that would last less than two minutes as the Reds failed to defend a left-wing corner and Naldo was free to head in his second goal of the game from another set-piece.
The drama was not over, as news filtered through that PSV went ahead and despite a late flurry, United go out.
Van Gaal said: “I haven’t thought about the Europa League at this moment. I’m very disappointed, the players are very disappointed.
“I think it was a crazy match. We had the chance to win, we fought for the win but with 10 men at the end, we couldn’t do any more than we did.”
It was an incredible finale and the culmination of a dramatic night which had seen United have a goal ruled out in the first half when teenage substitute Cameron Borthwick-Jackson, on for Matteo Darmian just seconds earlier, won the ball with his first touch, set up Lingard and his shot flew past goalkeeper Diego Benaglio into the far corner before the officials correctly ruled Juan Mata offside.
“I don’t think that the goalkeeper was interfered with by Mata because the ball was turning into the goal so I don’t think he can reach the ball,” said Van Gaal.
It was a cruel decision, especially as it took an age in coming, but one that was correct and it will have come to little consolation to United and their supporters that, after weeks of complaints about their team’s stale style of play, here were the famous old English club embroiled in a thrilling battle.
It had looked to have the potential for such after only three minutes when Max Kruse helped on a Vieirinha cross and Andre Schurrle was guilty of a bad miss with a hurried shot over from eight yards. That attempt had exposed full debutant Guillermo Varela, a shock selection by van Gaal in the right-back position, and the youngster’s vulnerability would continue.
First, though, United were offered a lifeline via Martial. It was a simple 10th minute goal, also, forged by the impressive Juan Mata who weighted a superb pass between the Brazilian central defensive pair Dante and Naldo for Martial whose finish was exemplary.
Just when United needed van Gaal’s defence to show the steadfast resolve that has been so evident in recent months, they failed. They held the lead for three minutes until a free-kick, conceded by Daley Blind, which defender Ricardo Rodriguez curled in for Naldo whose crisp, precise volley from eight yards was down not only to his superb technique but also some sloppy defending from Chris Smalling.
United remained undaunted and, in contrast to so much of this season, full of attacking intent. On 27 minutes, a fantastic Blind corner was met by Marouane Fellaini for a powerful header which Benaglio saved with a diving block.
That save proved all the more significant just two minutes when the Germans took the lead with a goal that was even more memorable than their first.
Two switches in play ended with Schurrle finding Julian Draxler, left to right, who played a one-two with Kruse and advanced to the corner of the six-yard area before squaring the ball for Portuguese international Vieirinha to convert into an open goal.
David de Gea was required to make a key stop to deny Draxler before the interval while, after it, the visitors played with even more urgency and directness. It almost paid dividends on the hour when Fellaini won a header from a Martial cross and, after Mata just failed to connect, Memphis Depay’s overhead kick again found Benaglio equal to the task with an acrobatic save.
United were almost undone a few moments later when de Gea rushed too far from his area to try and beat Schurrle to a through ball and then had to recover quickly and sprint back to save one-handed as the striker attempted to lob the ball over his head.
The game was becoming ever more open and United’s Spanish number one quickly saved from a Schurrle cross and a long-range effort from Max Arnold. A foul by Naldo on Martial brought United some respite although Memphis could only curl his free-kick inches wide of the right-hand post.
Benaglio 7; Trasch 7, Naldo 9, Dante 6, Rodriguez 6 (Schafer 16, 6); Arnold 7, Guilavogui 7; Vieirinha 7 (Klose 78, 6), Kruse 7, Draxler 8 (Caliguiri 84); Schurrle 7.
De Gea 7; Varela 6, Smalling 5, Blind 6, Darmian 5 (Borthwick-Jackson 43, 6); Fellaini 7, Schweinsteiger 5 (Carrick 68, 6); Lingard 6, Mata 7 (Powell 68, 6), Memphis 6; Martial 7. Referee: M Mazic 6