Australia's Channel Nine TV reported on Wednesday that the International Cricket Council was investigating the use of silicone, amid increasing controversy during the five-Test Ashes series over the inconsistency of the Decision Review System.
The ICC, cricket's governing body, issued an immediate denial and said the report was "totally incorrect".
"I think an apology is due for such a blatant fabrication," Cook told reporters on the eve of the fourth Test against Australia in County Durham.
"There has been a bit of a media storm behind it and we knew it would happen at some stage of the Ashes.
"It's kind of taken a little bit of the gloss off winning the Ashes ... but as players all that stuff is out of our control."
The series has been dogged by controversial umpiring decisions and there have been several occasions when Hotspot has failed to pick up edges.
England's leading batsman Kevin Pietersen was involved in one such incident during the third Test in Manchester when he was given out caught behind, even though nothing appeared on the Hotspot review.
Holders England, who are 2-0 up in the series and have already clinched the Ashes, are determined to put the furore over the Channel Nine report to one side for the penultimate game of the series.
"We're an experienced bunch of cricketers who have been through a lot as a side," said Cook. "There are a lot of players who have been through similar circumstances with a bit of controversy.
"We've dealt with it well in the past and I see no reason why we can't deal with it here. We've stuck together well and that's a sign of a strong team."
Cook called the Channel Nine report "absurd" and "blatantly untrue".
"Both sides have kind of laughed at it," he said. "Certainly we've been laughing at it in our dressing room because of how strange the story is.
"The mileage it's been given has been a bit strange and it's not great when you've been called a cheat as a side and have been accused of something you haven't done."
Australia skipper Michael Clarke concurred with his opposite number.
"I found it all quite amusing to be honest," said Clarke. "I prefer not to talk about it any more - you guys have had a couple of days to write and talk about it.
"For me the focus has to be on cricket. I think there has been enough good cricket been played this series and there is a huge Test match starting for the Australia team tomorrow."
Pietersen responded to the Channel Nine allegations by sending out a series of angry tweets.
"Horrible journalism yet again! My name brought up in Hotspot crisis suggesting I use silicon(e) infuriates me," he wrote on his Twitter feed.
"I am never afraid of getting out! If I nick it, I'll walk .... to suggest I cheat by covering my bat with silicon(e) infuriates me.
"How stupid would I be to try & hide a nick when it could save me on an LBW appeal, like in 1st innings where hotspot showed I nicked it."
Cook said he was fully behind Pietersen's angry response.
"I think he wanted to be sure he cleared his name pretty quickly," the England captain added. "He gave the story no legs and personally I think he was entitled to do that for something as stupid as that."
Channel Nine have refused to comment.
Cook has already amassed 25 centuries in his short Test career but the 28-year-old is still waiting to reach three figures in this Ashes encounter.
"At the top of the order it's your job to score runs and I haven't done quite as well as I would have liked in this series," said the left-hander.
"I've been working hard on my game like I always do. What I do know is I've scored runs in the past and my test career shows I've scored runs so hopefully it's just a matter of time.
"In our eyes the series is still very much alive. We set out to win the series, not just to win the Ashes, and that's still the goal," said Cook.