Claude Puel felt that Leicester City were denied a blatant penalty at the King Power Stadium.
Rafa Benitez's side were leading 1-0 thanks to a first-half strike from Shelvey when Riyad Mahrez went down in the box under a challenge from Paul Dummett.
Referee Stuart Atwell, however, waved played on. Perez went on to score a second goal for United in the second half, and Jamie Vardy netted a late consolation for the home side.
"Of course it was a penalty,” said Leicester manager Puel, who also acknowledged that his team was "poor".
“There was contact with the foot of Riyad. For me, it was a penalty.
“It was an important moment to come back into the game just before the break and to start the second half with a good feeling and good mentality.
"This decision could have helped us come back into the game with a good tempo and a good feeling in the second half. It could have given us a boost.
“It was not enough, but it's not just a question of the penalty. It is not an excuse, because our performance was too poor in the first half and we have to correct that aspect of our game."
Leicester defender Harry Maguire was only shown a yellow card for striking Newcastle's Dwight Gayle.
The contact appeared to warrant a red card, but Puel said it was the "right decision".
United manager Rafa Benitez said: "I have had players sent off just for touching the face of a player.
"I cannot argue too much, and the main thing for us was the performance of the team. We deserved to win."
The result moved United up to 10th place in the Premier League.