Poyet has joined Milton Keynes Dons on loan until the end of the season, and Robinson says that he would be keen to make the move a permanent one.
The Uruguayan has gone straight into the Dons' team since arriving, and his performances, alongside fellow loanees Jake Forster-Caskey, Josh Murphy and Rob Hall, have impressed Robinson.
“I’d love them to be ours,” he said. “I’d like to go out and get them all, that would give us a fighting chance to be competitive in this league.
“We’ve got to find and sustain players of that ilk, that are ours, if we want to remain at this level.
“I’d love to see what they could all do together."
Poyet has already made 10 appearances in his time at stadium:mk, and he will be hoping to continue playing a prominent part for the Championship side as the season progresses.
The 20-year-old has been thrown in at the deep end, but he was able to help MK to an impressive 3-0 win over Blackburn Rovers in their latest outing.
There is no suggestion that West Ham would be inclined to sell the midfielder at the end of the season, though, so Robinson may be left disappointed if he did enquire over a permanent deal.
The Hammers have high hopes of their own for Poyet, who has made 10 senior appearances for their senior side to date.