The Gunners are currently third in the table behind Leicester City and Tottenham Hotspur
The Gunners were beaten 2-0 at the Emirates on Tuesday evening, as two goals from Lionel Messi put the Catalans in a commanding position in the tie.
While they are far from out of the Champions League just yet, not many are expecting Arsenal to progress given the current situation.
And Ferdinand says they must instead turn their full attention to the Premier League and win that, or serious questions will be asked at the club.
“Going out to this Barcelona team, you can’t really judge them on that,” he told BT Sport.
“But the Premier League has been so inconsistent, especially from the top teams such as Chelsea, Manchester City and Manchester United, this is the year they should go on and win it.”
“If they don’t, then I’m sure that questions will be asked. “
If Arsenal can win the Premier League however remains to be seen, with this season’s race looking to be one of the closest in a number of years.
They are currently 3rd in the table, level on points with Tottenham Hotspur in 2nd and trailing leaders Leicester City by two points.
The competition is fierce, with the Foxes looking definite challengers and Spurs continuing to impress under Mauricio Pochettino.
Should either of those, or even Manchester City, finish ahead of Arsenal, it will certainly be interesting to see if people will question Arsene Wenger in particular.