It's believed The CliffsofMoher suffered a fractured right shoulder.
"This is all down to Sheikh Mohammed, he's the one that's given us all the encouragement to take the chances in what we do internationally", Appleby said.
After turning into the straight among the tailenders, Cross Counter finished with a withering burst down the outside to record a stunning win, outlasting another United Kingdom star, Marmelo.
"I think we certainly should consider it", he said.
Appleby was appointed as a Godolphin trainer in July 2013, after 15 years working for Sheikh Mohammed as a travelling head lad, stable head lad and assistant trainer.
The Cup had always been the nut that Sheikh Mohammed could not crack despite trying to hit it with a sledgehammer on plenty of occasions.
Dubai ruler Sheikh Mohammed bin Rashid Al Maktoum is the backer behind Godolphin, the biggest thoroughbred racing operation on the planet. I can't believe it - I'm over the moon.
Appleby has not had time to think about becoming the first English trainer of a Melbourne Cup victor, with his focus on the significance of the win for Sheikh Mohammed and Godolphin.
"I'm just lucky to be in a position to train these horses", said Appleby.
It is the fourth time in the past six years that the Cup has been shrouded by the death of horses.
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Cross Counter won the Cup, the Charlie Appleby-trained stayer handing Australian jockey Kerrin McEvoy his third Cup triumph.
"It is a very special day for us all".
Viewers reacted in horror after the Melbourne Cup hopeful pulled up lame in a mid-race mishap.
He returned past year, with success, and for the 2018 spring carnival had an early victory with Jungle Cat at Group One level.
In 2014 two horses Admire Rakti and Araldo were put down following the race. "Hindsight is showing to us, maybe not financially, it was the right decision in skipping the Caulfield Cup with him".
Animal welfare groups led the calls for an inquiry into the death of The Cliffsofmoher, which was one of the leading fancies heading into the Melbourne Cup but was a late betting drifter after sweating up in the parade.
For jockey Kerrin McEvoy, it is his third Melbourne Cup, and he becomes the first jockey to complete the Everest-Cup double.
"Coming into today, this horse ticked a lot of boxes".
The Newmarket-based Appleby, who gave Godolphin its first Epsom Derby victor, Masar, in June, added: "This is huge for everybody". Well done to Charlie and this little horse.