Davis posted a team-high six catches for 86 yards and one touchdown in the win. Cooley did not record a single catch for only the fifth time in his career.
Shanahan was asked if Fred Davis had supplanted Cooley as the No. 1 tight end on the depth chart.
“We don’t go through our depth chart for obvious reasons," Shanahan replied. "In the game, we had two tight ends start – both Fred and Chris. We have two excellent football players.”
Cooley was sidelined during preseason due to a knee injury and he was limited in practice up until the week before the season opener against the New York Giants.
Cooley is getting healthier, Shanahan said.
“He’s getting in better football shape and I think it was good for him to play a number of plays," Shanahan said. "I liked the way he performed. Chris is a very unselfish guy. In fact, in the second quarter, he said, ‘Hey, I think we need to get Fred the ball.’
"He was a little frustrated and we had a couple of plays in the game plan designed for Fred, and Chris kind of alerted me, so that shows you the type of mindset Chris is in.”
Shanahan said he isn’t worried about figuring out playing time for two starting-caliber tight ends.
“Like I said, those are the problems that you want," he said. "We will play the best players. If we have four tight ends that are our best players, then we won’t have wide receivers out on the field.
"If we have four wide receivers that are great players and our tight ends aren’t playing at a certain level, then we’ll have four wide receivers [play]. We have the type of flexibility on offense to do what we want to do."