The defeat was the Gunners' third Premier League loss of the season, with their former striker Robin van Persie opening the scoring for the hosts after a mistake from defender Thomas Vermaelen, and Shearer has questioned whether Arsene Wenger's side are any longer in the top bracket of clubs worldwide.
Shearer told The Sun: "Which other big club around Europe would sit by and continue to employ a manager who has not won a trophy in seven-and-a-half years? Or do Arsenal no longer put themselves in their category?
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"It is the ease with which their best players have walked out the door at the height of their powers that is so worrying — and the replacements have not been up to it.
"People like Van Persie, Cesc Fabregas, Samir Nasri, Gael Clichy, Kolo Toure and, soon, Theo Walcott. The Bosman ruling can often take things out of the manager's hands but why are the players allowed to get to a point where they can use it?
"If the team was successful they would not be even looking at the exit door and therein we have the biggest problem. There is nothing to suggest this Arsenal side is going to change that trend.
"The DNA has gone out the side. Arsenal just seem on a continual slide to a point where they are not even considered contenders."
Shearer also strongly criticised Arsenal left-back Andre Santos, who could be seen swapping shirts with Van Persie at half-time.
He added: "I couldn't quite believe what I was seeing. He's 29, not a young naive lad. He was absolutely all over the place on Saturday as were the whole Arsenal team in terms of defending."
He went on to question the side’s mentality, contrasting Wenger’s fortunes with his counterpart at Old Trafford, pointing out: "Alex Ferguson also had a barren spell, when he went three seasons without the title between 2003 and 2007.
"People were even questioning him at that stage. But he rebuilt and produced another all-conquering team.
"You could argue this Manchester United team does not compare with that of 1999-2001 or of 2008 that had Cristiano Ronaldo in it. What it still has is that steel, desire and will to win."