Manchester United won Wednesday's second leg against Bayern Munich 3-2 but failed to make the UEFA Champions League semifinals.
The narrow victory left the United drawing 4-4 on aggregate with Bayern but the latter advanced on away goals.
It will be the first time since 2003 that the Champions League won't feature an English team in the final four, while Bayern the first German team to make it since 2002.
Bayern will host Lyon in the first leg of the semis on April 21 with the return leg six days later. The latter lost the return leg 1-0 at Bordeaux but headed through 3-2 winners overall to reach its first semifinal on Wednesday.
The other semifinal pit Barcelona and Inter Milan on April 20 and 28 after the duo claimed respective victories over Arsenal and CSKA Moscow on Tuesday.
At Old Trafford, Bayern trailed 3-0 before losing 3-2 as Wayne Rooney surprisingly started for the United after injuring his ankle in last week's first leg.
"It was an incredible comeback from three goals down," Bayern coach Louis van Gaal said.
The hosts wiped out Bayern's 2-1 advantage inside seven minutes after goals from Darron Gibson and Nani before the latter gave the United a 3-0 lead in the 41st.
Ivica Olic started the visitors' comeback two minutes later, and Arjen Robben scored from a volley in the 74th minute to the German through.
The United, last season's runners-up, played with 10 men after Rafael da Silva was sent off in the 50th for fouling Franck Ribery to receive a second yellow card.