Pietersen revealed in his book that he was bullied by Matt Prior, while other members of the Three Lions team were accused of mocking the 34-year-old in a parody Twitter account.
Cook told BBC Sport: "International cricket is a tough place and, as a team, you're striving for excellence at all times.
"Certainly at some stages those frustrations boiled over more than they should have done, but that was only people who were desperate to succeed and wanting to know the other 10 blokes around them were committed 100% to it also.
"Did it overstep the mark a couple of times? Possibly, but we addressed those issues. That's what happens in teams, but it certainly wasn't a bullying environment as such."