Manchester United have already had two bids rejected for the Barcelona midfielder, the latest for around £30m.
Moyes felt Fabregas was keen on a switch to Old Trafford due to fears he would not play regularly in Spain this season.
But the United boss is now planning to accept defeat after being forcefully told by new Barcelona coach Gerardo Martino that the 26-year-old is not for sale at any price.
“I couldn’t tell you if there will be another bid,” Moyes said. “We will take stock of it and consider what we are going to do next.
“I never said at any time that we would get him. I just said we had made offers – and they have been rejected.”
Business Moyes is now poised to look elsewhere to strengthen his midfield, while also rejecting an approach from Borussia Dortmund for Shinji Kagawa.
Dortmund boss Jurgen Klopp yesterday admitted an enquiry was quickly turned down, with United keen to bolster their squad rather than weaken it.
The the new Old Trafford boss said: “I did not necessarily think we would have new players by now. We hoped we would do, of course, but what we have here is a really good squad of players.
“Undoubtedly we’re hoping to add to it and we’re confident we will do so before the window shuts. We’ve got until September 2 – that’s the deadline – so I’m confident we’ll have players in.
“But I’ve got a squad that finished 11 points clear at the top of the Premier League, so I’m confident of going into the season with that.
“I have got a few more players that I have not even met yet.