Ex-Gunners midfielder Ljungberg, 42, is in interim charge of the club after they sacked Unai Emery last month.
"Freddie said he was 100% sure they would get into the top four but based on what? It's fantasy," said Sutton on BBC Radio 5 Live's Monday Night Club.
"They need to get someone in place that they are going to get a reaction from."
Ljungberg, who played for Arsenal between 1998 and 2007, had been Emery's assistant after working with their under-23 side but has no previous managerial experience.