The Gunners surrendered their Premiership lead this week, but Diaby says: "I think we can win the Premier League and Champions League.
"Arsenal are a big club and we want to be first in every competition."
He added: "Of course, it is better to have a player like Thierry Henry in your team. He can make the difference at any time during a game.
"But he has left and the players have had to take on more responsibility. The players have more experience now, compared to last season, and we have learned from our mistakes."
Diaby has dismissed claims he will be on the move in the summer.
He insisted: "I want to stay at Arsenal. I feel good here."