The Uruguayan thinks his side should have had a penalty during the 2-1 loss to Tottenham Hotspur.
New signing Jermain Defoe had a penalty appeal turned down, meaning he missed out on the opportunity to score his first goal for his new club - against his old club.
The striker tumbled over Tottenham defender Jan Vertonghen’s outstretched leg in the box but his appeals were turned away by the referee, leaving manager Poyet to fume at the decision.
"He started brightly, he was sharp,'' Poyet told reporters.
"If he got the penalty and he scores, we're talking about a great debut. The referee, though, didn't see what everybody else saw clearly.”
Sunderland boss Poyet, however, was enthused by his new signing's performance and feels that it won’t be long before the former Tottenham and England man nets his first goal for the club.
"It was a good start and a great place for him to start playing for us," said the Uruguayan.
"He will get better and better, and when he gets that first chance he will put the ball in the back of the net.
The loss leaves Sunderland 16th in the table, just one point above 18th-placed Hull, who play West Ham on Sunday.