The Gunners have conceded 14 goals in five games, highlighted by an 8-2 loss to Manchester United, and culminating in the weekend's capitulation at Ewood Park.
Graham is known for building an Arsenal team based on their back four and feels that Wenger messed up by strengthening his squad late in the transfer window when he should have done it earlier in the summer.
"I think they left it a bit late to bring in all these players," he told BBC Radio Five Live.
"Two weeks of the season had gone by, and he's not had time to work with the players he's brought in.
"Defensively they've not had enough time to work with the back four."
Graham added: "It's been generally known they had to shore up the defence.
"Some of their attacking play is still the best in the league, and even at the weekend against Blackburn some of their possession play was fantastic.
"But again the old problems defensively cropped up and they lost 4-3."
And Graham was also critical of the way the North London club went about things during the summer, knowing very well that star players Cesc Fabregas and Samir Nasri were set to leave the Emirates Stadium.
"Everybody knew they were on the way out way before the beginning of the season," he added.
"I would like to know who was responsible for the approach to the new season."