"To not be in the Champions League next season would be a very disappointing situation for us, but we will fight until the end to have as much of a chance to be there next season," Koscielny told Sky Sports.
"The Champions League is a competition that a player wants to play in because you play against the best teams in Europe and it is always an important competition.
"We need to do our job first, to have the two wins, and after that we wait for the results of Liverpool and Man City."
City are currently in fourth place, three points ahead of Arsenal. Liverpool, who have played a game more, are a point above them in third.
Arsenal face relegated Sunderland later on Tuesday, and can still add a trophy to their cabinet this season by beating Premier League champions Chelsea in the FA Cup final on May 27.
Koscielny also said he was nursing a long-term Achilles injury that will affect him for the rest of his career and hinted he was ready to sit out Tuesday's clash to save himself for the cup final at Wembley.
"I have some problems," he added. "Every morning, I have my treatment for my Achilles and I know I need to do this to the end of my career.
"I am prepared to miss Sunderland to be fit for the last two games of this season. Sometimes it is better to miss one game to be fit for the others."
Arsenal end their league season at home to Everton on Sunday.
(Reporting by Simon Jennings in Bengaluru, editing by Larry King)
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