Obama made the call a day after the Cardinals were beaten by the Steelers in Sunday's Super Bowl.
Whisenhunt said the call came shortly after he returned to his home Monday afternoon.
He said Obama was "congratulating our team on the success we had had and was very impressed with the way our men had played. And that was quite special."
"I was actually just walking in my front door," Whisenhunt said Tuesday. "He called my cell phone. I don't know how they got my number ... I was humbled and I was stunned."
Obama proved prophetic when he was interviewed by Matt Lauer on NBC's pregame show Sunday.
"I think the Steelers are going to eke it out in the end," the president said before Arizona rallied to take a 23-20 fourth-quarter lead, only to fall 27-23 on Santonio Holmes' tiptoe catch for a touchdown with 35 seconds to play.
Obama had conceded earlier in the week that he was pulling for Pittsburgh. Steelers owner Dan Rooney, a longtime Republican, endorsed Obama's presidential bid and campaigned for him.