The former Gunners sporting director resigned on Monday after five years with the club.
"The plan and vision, that starts with the ownership, that is very clear and very ambitious is going to continue," Arteta said.
"We have a very strong leadership team with an unbelievable know-how, a real passion and great feelings for the club, we're not going to stop where we are at the moment.
"Across the club, the excitement, the passion, the understanding of where we want to take this journey remain intact."
Arteta added, "From day one, we've been together and I'm very grateful personally for everything he's done for me and the amazing work he's done for the football club.
"We both had this special chemistry working together.
"I'm very blessed that he's been part of my life in such a beautiful place, managing this incredible club. He's been a massive part of that.
"He's had an amazing opportunity now to do something else in a different role. He believes that's the right professional move for him. We have to respect that. From that bottom of my heart, I think everybody feels that we want the best for him."