The Gunners have been left to fight for second place in the Barclays Premier League at best as their title hopes and dreams of Champions League glory have dissolved in recent weeks.
He told BBC Radio 5 Live's Sportsweek show: "Arsene has got to sit down and be honest with himself, which I am sure he is.
"After three-quarters of the season, they were five points clear, absolutely over-achieving, and then in the run-in, they are stumbling all the time.
"He must look back and ask: 'did the players get tired? Why did they get tired? Did he have a strong enough squad? Were they too inexperienced to get over the white line and win the trophy?'
"He needs, in my opinion, three or even four ready-made players, which will cost a lot of money - and that may be a problem because I don't know if Arsenal have got a big budget to get new players in next season.
"Certain players at Arsenal keep on getting injured, and you know next season, the same players will probably be on the treatment table a lot.
"I think he needs three or four, and I think he needs three or four ready-made players, star players who are going to cost big money and big salaries, which will not go down well at Arsenal."
Asked where he feels Wenger needs to strengthen his squad, Graham replied: "Through the middle, the spine of the team.
"They need a world-class goalkeeper, they need a centre-half, they need more mental and physical strength in the middle of the pitch.
"Unfortunately, their strikers seem to be picking up a lot of injuries, so they need somebody to play alongside (Emmanuel) Adebayor, who I think could develop into a world-class player."