Arteta has overseen Arsenal's worst start to a season in 118 years this term, the Gunners losing their opening three games, scoring zero and conceding nine in the process - but the rut appears to have stopped, at least for the time being after successive wins over Norwich and Burnley respectively.
Speaking to The Beautiful Game podcast, Mertesacker said: "I hope Mikel gets the time that he needs.
"When you look at it from a case of 'first managerial job – Arsenal football club', where you would hope you have people with experience to know how to deal with these adverse moments, how to deal with successful moments like winning the FA Cup.
"I think sometimes it is difficult to explain but what Mikel gives you is a hell of a lot of experience as an assistant coach under Pep Guardiola – he wanted to make that next step and people, hierarchies trusted him."
Mertesacker did go on to concede that Arteta will be in "trouble" if he oversees another three game losing streak again.
"He presented himself as someone who wants to lead us into these difficult moments so I could only agree but if I had known, how he reacts to difficult moments – he needs to learn fairly quickly, let's be honest.
"He needs to learn super, super quick because in football, and being manager of Arsenal football club – if you lose three games on the spin, you are in trouble."
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