"It was a demonstration to Arsenal fans," said Keown.
"The club were saying 'We have £40m there. We have tried to buy someone else's best player for a change'. It has shown how serious Arsenal are about spending money.
"Now he needs to go out and buy an obvious talent, someone who is going to hit the ground running, and they don't come cheap.
Keown highlighted the impact made by Dennis Bergkamp when he joined Arsenal in 1995.
"Arsenal won 10 and drew two of their final 12 games last season. That was championship form," added Keown.
"I just feel if you are in the camp, you need a new signing, someone who makes you believe you are going in the right direction.
"It happened for us with Dennis Bergkamp. People asked why we were signing him.
"They didn't think he was going to be there for long but he ended up being one of the most successful overseas players ever to play in the Premier League.
"Maybe someone else can come in and do the same thing."