IRVING, Texas -- Phil Costa had an MRI to determine the severity of the back injury that tightened up after three snaps in Wednesday’s win against the New York Giants, but Cowboys coach Jason Garrett was not ready to say the center position is open for competition.

“I don’t want to get into that right now,” Garrett said. “We want Costa to get back. Costa’s been our starting center for a reason. We like him a lot. But at the same time, we want to make sure he’s healthy. I thought he did a really good job working to get back and it just shows you the kind of mental toughness that he has. He was determined to play, and his back really wasn’t quite right. We really found out about it on the first play. He tried to gut it out on plays two and three, but then we had to put Ryan in on the second series.”

Costa missed the first three preseason games because of a low back strain but was able to get 12 snaps of work in the Miami preseason finale. The Cowboys acquired Cook in a trade from the Dolphins after the game, but he had just a handful of walkthrough snaps with Tony Romo before being forced on the field.

“One of the reasons we liked him is he’s a veteran player,” Garrett said. “He’s been a center in this league. He’s also played guard and tackle and we felt like he could go into a game with short notice. He picked things up fairly well last week in the practice reps that he did get.”

The Cowboys had five false-start and two delay-of-game penalties against the Giants that could partially be attributed to Cook’s unfamiliarity with Romo and the offense.

“Obviously communication is really important for those guys up front, but he’s a smart guy,” Garrett said. “I think he understood the concepts right from the start. The biggest thing was the communication, using our language, but I think he studied hard at it. They communicated well together. There weren’t a lot of busts that way in the ballgame.”