The skipper was bombarded with questions about Pietersen during Saturday's news conference as third-ranked England prepared to take on second-ranked Australia in a five-game ODI series starting on Sunday at the MCG.
Pietersen is being rested from the ODI series and the England camp has been fending off reports in the past week of the 104-Test veteran causing unrest in the change rooms.
Cook, who led England to a five-nil defeat in the Ashes series completed on January 5 in Sydney, has received strong backing to continue in the top job.
However, the skipper refused to give similar backing to 33-year-old Pietersen to stay on in his Test team.
Given the chance on Saturday to correct any misconceptions about Pietersen's attitude in the change rooms, Cook shouldered arms.
"I can't talk about what happens in the dressing room at this precise moment in time. I refuse to do that," Cook said.
When questioned about whether this hardly looks like an endorsement of the controversial South African-born superstar, Cook added: "You can regard it as you want."
Cook says he needs to move on quickly to thinking about the ODI series and the 2015 World Cup hosted by Australia and New Zealand.
"When you lose a series five-nil, a lot of things get thrown up and thrown in your face as a captain," he said.
"We know that when I get home from this one-day series, a lot of important decisions on how we want to go forward with this Test team, the one-day team and my future -- all that kind of stuff -- is very important.
"My total focus has to be on us winning games of cricket in this series.
"We have a World Cup in 2015 in exactly the same conditions as we are going to experience here and that has to be given my full thought."
Asked about his rapport with Pietersen, Cook said: "We've had a good relationship.
"It's very hard for me to talk to you, the media, about this," Cook said.
"I can't do that. Confidentiality and stuff like that -- what happens in the dressing room stays in the dressing room."
Cook says it is not the time to talk about the Test team.
"I know you are going to drag me back there," he told reporters.
"We came here to take the Ashes home.
"Now that we've lost them, if we win this one-day series, we salvage some pride from our performances.
"There's a lot of guys who haven't been affected personally by the five-nil.
"There is a change of mood, there is an upbeat nature and excitement to start the series, as you would expect."