The Gunners looked to be heading for victory when Hector Bellerin gave them the lead early in the second half.
Serving the final game of his three-match touchline ban, Arsene Wenger watched from the stands as his side lost crucial ground in the race for Champions League qualification. Jordan Ibe scored the victor minutes later.
Arsenal have endured a curious week, having been dumped out of the FA Cup by Championship side Nottingham Forest before recording a creditable goalless draw at Stamford Bridge in the first leg of their Carabao Cup semi-final.
It would also be folly to think that Sanchez can be adequately replaced - certainly in the short term - by Bordeaux's Malcom, who although supremely talented is only 20 and would arrive at Arsenal with no Premier League experience.
Arsenal now switch their attentions towards preparing for their home clash against Crystal Palace on Saturday afternoon.
"When you start taking the really top players who can really turn a game away, you've got to fill that spot and it's not easy to do that in January".
Winning the League Cup would be Wenger's 11th major trophy as Arsenal boss and he has never won the competition before.