A late goal from Kevin Grosskreutz gave Borussia Dortmund a 2-1 win at the Stade Velodrome on Wednesday, a result that ensured Marseille finished this season's Group F pointless, while the German side progressed as group winners.
Dortmund's winner came after Souleymane Diawara had cancelled out Robert Lewandowski's fourth-minute opener.
And Anigo believes the Ligue 1 club can hold their heads high, despite becoming the first French team to finish the group stage without earning a point.
"What changed tonight compared to the other games is the state of mind," Anigo told Canal +.
"When they decide to give it their all, it is a different game.
"At ten against 11, it became very complicated.
"But there is nothing to be ashamed of because we gave everything."
Marseille will hope to get back to winning ways when they travel to Lyon on Sunday.
