Muker is likely to be put away until next season following his fine effort in defeat at Dundalk.
A narrow winner on his racecourse debut at Newcastle, the Mehmas colt came close to providing fledgling trainer Phillip Makin with a first Royal Ascot success when a close-up third in the Windsor Castle Stakes in June.
Muker got back to winning ways on his next start, but was subsequently sidelined by injury for three months.
However, he proved he had suffered no lasting damage when just narrowly denied by Urban Beat in the Group Three Mercury Stakes, which was this year run in memory of Pat Smullen, and Makin is already looking forward to seeing what his stable star can achieve in 2021.
He said: “He had a setback after York, which was a shame, because it meant he missed the back-end of the summer when he might have been busy.
“We took him to Ireland last week, because there was basically nothing else for him, and he was half-learning on the job.
“We were really pleased with how he ran. It was a tough ask for him, taking on those older horses, so it was nice to see him run so well.”
Remaining opportunities to run this year are scarce, and Makin is minded to stay patient.
He added: “There is a Listed race at Chantilly on November 10 we could run him in before the end of the year, but the ground could be ploughed and I think we’ll probably just put him away until next year.
“He’s obviously been a sharp two-year-old, but Declan (McDonogh) was quite complimentary about him the other day and said he thinks he’ll train on, so hopefully he’s right.”