After struggling to land high-profile signings during the transfer window and early season losses to rivals Liverpool and Manchester City, the Scot's ability for the job has been questioned by some.
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"If Manchester United had made the best ever start in their history there would have been people complaining," he told talkSPORT.
"Manchester United fans are very loyal and it takes a long time for them to forget certain things. Sir Alex Ferguson has been a massive part of that club for a long time, but he had his bad times, too. This will take a little bit of time."
Bosnich also highlighted the need for his former club to be active in the January transfer window, following public failures to secure the likes of Thiago and Cesc Fabregas during the summer.
"They missed out in the transfer market and, if you look at teams like Arsenal, who signed Mesut Ozil, they looked a completely different team. The January transfer window will be a very interesting time," he added.
"They have known for some time that, in the big games, they need a few more players. They need to make themselves difficult to beat."