Arsenal look set to miss out on the Premier League top four for a third successive season.
However, they can qualify for the Champions League if they win the Europa League.
Robson claims the recruitment at Arsenal has not been good enough in recent years, though he admits Lucas Torreira and Matteo Guendouzi appear to be top prospects.
He says Granit Xhaka is not good enough to play in defensive midfield and Shkodran Mustafi is not up to scratch at centre-back.
And Robson admits club captain Laurent Koscielny, 33, and fellow defender Sokratis Papastathopoulos, 30, are coming towards the end of their careers at the top level.
“Is Xhaka athletic enough to be a holding-midfield player? In my view he’s not,” Robson told talkSPORT on Thursday.
“Torreira I think will be a good player but he’s not always played him.
“Guendouzi would probably be a very good player over a period of time.
“But they’ve got problems defensively.
“Mustafi’s not been good enough, Koscielny’s coming towards the end of his career, although he’s had a good few games recently.
“Sokratis I thought was a good player at Borussia Dortmund but again he’s coming towards the end of his career in some ways.
“The recruitment needs to be much better.”
Arsenal lost their head of recruitment earlier this year when Sven Mislintat quit the club.
Former midfielder Edu appears set to take over as technical director in the summer and Robson says big improvements in the transfer market are needed.
“[Mislintat] had an argument I think with Unai Emery, Unai Emery and him didn’t really see eye to eye about the players they were buying and what the job was of Mislintat,” he continued.
“So that’s another problem for Unai Emery and a problem for Arsenal.
“Are they going to resolve it by the start of next season?
“They’re going to have to if Arsenal want to challenge for the Premier League title, if they want to challenge the Europa League again or Champions League if they can get into that.
“So it’s a big job for Unai Emery and the people above him.”