Barca defeated the capital giants in the Champions League semi-final, 3-1 on aggregate, before overcoming Manchester United in Saturday's final to widespread acclaim.
Khedira told Kicker of his belief that Madrid are within touching distance of the Catalan giants, and added that the team would not have lost 2-0 to Barca in the first leg of their Champions League tie had Pepe not been "wrongly" sent off.
"Everyone agrees that Barcelona deserved to win the Champions League, but we don't need to improve much to get to their level," the German said.
"In the [semi-final], we lost as the result of a red card that, in my view, was wrong. If we had played with 11 men against 11, we would not have lost the game."
Pepe was sent off for a late challenge on Dani Alves after 61 minutes in the first leg at the Santiago Bernabeu, before two Lionel Messi goals won the match for Barcelona.