Leigh's character Lexie Grey was killed off in the show's eighth-season finale, while Raver's Teddy Altman also departed the series.
"Chyler is a very dear friend - she and I have always been such good buddies," Drew told TVLine.
"And Kim has been an unbelievable support as I went through pregnancy and early parenthood. She went out of her way to care for me and give advice, so I was tragically sad to see her go."
Drew admitted that the loss of Leigh and Raver makes her feel "trepidation" that her own character April Kepner could also be written out.
"Anybody can go at any time, especially on Grey's," she said. "But I'm really glad I didn't get killed off."
Grey's Anatomy will return to CBS with new episodes in late 2012. The series airs on Sky Living in the UK.