Arsene Wenger's men went out of the Champions League to Bayern Munich on away goals despite a 2-0 win in Bavaria, meaning their focus now turns to securing a spot in next year's competition.
The north London club currently sit fifth in the table, five points adrift of fourth-placed Chelsea, and Laudrup believes they cannot afford give up any more ground.
"Chelsea are at home this weekend, so if they win and Arsenal don't win here, they would be eight points behind and with only nine games to go that may be too big a gap," he said.
"So it is a very important game for them to keep alive the possibility of going into the Champions League next season."
But Laudrup gave his backing to counterpart Wenger, despite the club's eighth season without silverware.
"He (Wenger) has been there 17 years now," Laudrup added. "If the fans want trophies then eight years is of course a long time but what he has achieved there is great.
"He has been there for so long because people have been pleased with what he has done, and I think we will still see Arsene Wenger on the Arsenal bench next season."