The New Approach colt became the first horse to carry the royal blue silks of Godolphin to victory in the Investec Derby at Epsom last season, but a leg injury kept him off the track for the remainder of the campaign.
Masar made his long-awaited return in the Hardwicke Stakes at Royal Ascot last month - and having run with credit to finish fifth after stumbling soon after the stalls opened, he was a hot favourite to get back on the winning trail in Thursday's Group Two feature.
However, Appleby's ace finished last of six runners and connections are keen to let the dust settle before making future plans.
"He came out the race well and there were no problems at all. The discussion will go on over the next week before we make a decision on what lies in his future," said Appleby.
"At the end of the day he is a horse that owes us nothing and he gave us a fantastic day last year (at Epsom). On the flip side of that, his work last week was so good we came into this meeting confident that we would hopefully get him back on the winning track.
"He has had two starts this year. The first was a messy race for him - having the start he did - and this time we got trapped wide and ran too free. It would be lovely to see him have another crack at it where he can get himself into a lovely rhythm and we can see what he has done before.
"No one will change my mind at all. Does he still have the ability? Yes. The main thing is he has pulled up sound.
"The York Stakes in a couple of weeks' time will come too quick, so at the moment, there is no real set plan."