"I don't think anything like this has happened to any team in the world," Edgar Ospina, whose side are one off the bottom of the Peruvian championship, told the website of El Comercio newspaper.
"We deserve to be in the Guinness Book of Records. I've never seen anything like it."
Union's latest blooper came on Sunday when Argentine defender Joaquin Lencinas side-footed the ball into his own net from six metres to condemn his side to a 1-0 defeat against Leon de Huanuco.
Goalkeeper Juan Flores began the embarrassing sequence two weeks ago in a 2-0 defeat against Sporting Cristal with a spectacular blunder.
Having collected a back pass, Flores took a back pass and nonchalantly dribbled the ball to one side of his box before missing it completely as he went to kick to a defender, allowing an opponent to nip in and run the ball into an empty goal.
In the following match against Universtario, one of the opposing strikers appeared to be tripped in the Comercio area and Renzo Reanos hoofed the ball into his own net in anger, apparently thinking the referee had given a penalty. It was the only goal of the game.
Ospina said that the incidents had at least earned international publicity for team, whose name translates as "Commercial Union", after gaining hundreds of thousands of views on Youtube.
"There's just no explanation for it. In football terms, we have been better than our opponents, we haven't taken our chances, but there's nothing you can do about this type of thing," he said. "Our players aren't robots."
"Fifteen days ago, they thought we were an organisation of shopkeepers. At least, now they know we are a football team."