The 18-year-old Frenchman made five appearances for the Pilgrims, including victories over Hereford, Darlington and Brackjley Town, as well as the defeat at Chester and draw with Chorley.
He also won two man of the match awards.
"Loick has been superb," Elliott told bufc.co.uk.
"I am sure he has learned a lot. I am really disappointed that he is going back - but he goes back with our best wishes.
"Hopefully he can get into the first team. That's the pathway - they come to us to learn and get that experience and he has done that.
"I know Huddersfield have been really happy with him. He's been a great character and I wish him nothing but the best."
Replacing Ayina will be Kyron Gordon, who made his Pilgrims debut off the bench at Brackley this weekend.
The 19-year-old has made two first team appearances for the Blades.
"We have been after Kyron for a while," Elliott added.
"I have watched a lot of him in the under-23s at Sheffield United.
"He gives us good balance and knows the system we are playing at the moment."
MORE PILGRIMS: Shane Byrne reflects on victorious Brackley return - news
MORE PILGRIMS: Elliott praises heart and character after Brackley win - news
MORE PILGRIMS: Brackley 1 Boston United 2 - report
MORE PILGRIMS: Sheffield United defender joins United - news