The Brazilian defender finalised his move to the Gunners on the transfer deadline day, joining the London-based club for £8 million on a two-year contract.
"We had some conversations over the last week, honest ones and the conclusion was that he should move on," he said at Friday's pre-match news conference.
"It's a position that I have a lot of competition in. Everyone has to understand that. He has moved on and we wish him the absolute best, because he has been a big part of our history.
"There wasn't any strikes. No fall-outs, just honest conversations. As a player I want that as a manager and I think I got that from David. Him not training was a decision I made."
After revealing the 32-year-old did not force his move from the club, Lampard commented on the club’s two-window transfer ban as he believes Chelsea are not considered as the favourites to win the Premier League title.
"It is what it is.
"We have to remain competitive while we are in this position.
"With the ban it has been easy to write off this squad, and I don’t write off this squad at all. I think that what is important is that you have a target within the group. What matters is how we approach things. We will see how we go."
Chelsea will begin their new Premier League season with a game against Manchester United at Old Trafford on Sunday.
