Tennis great and best-selling author John McEnroe, 43, is avoiding directly answering his ex-wife Tatum O'Neal's accusation that he used steroids while playing on the pro circuit, reports Reuters. But he did suggest Wednesday that it was sour grapes over what he says about O'Neal in his new book, "You Cannot Be Serious," that led her to speak out against him. (There will be much more coming from O'Neal in the new PEOPLE, which goes on sale Friday -- with O'Neal on the cover.) Speaking to reporters in a conference call prior to his covering Wimbledon for NBC, McEnroe insisted that for the sake of his and O'Neal's three children he would not discuss the particulars of her allegations, Reuters reports. As PEOPLE.com reported on Wednesday, O'Neal, 38, mentions McEnroe's alleged steroid use to Barbara Walters in an interview to air Friday night on ABC's "20/20." In a statement Tuesday, McEnroe said he was "disappointed in Tatum's statements." He did not directly rebut their accuracy. (Just as O'Neal, in her PEOPLE interview, claimed that a lot of what McEnroe says in his book, about her temper and drug use, is true.) "I had hoped that after all these years she would see things more accurately and that she would share my concern for the welfare of our children," his statement went on to say. Pressed by reporters for more information Wednesday, McEnroe said, according to Reuters: "I think my statement makes pretty clear as to what my feelings are on that topic, as well as other ones, but unfortunately, it's not as simple as addressing this one issue, and I believe I'm better served, and my family and children are better served, by sticking with what I said."