The 49-year-old, who has starred on the show since its 2005 debut, admits the first decade of the show was all drama as castmate Katherine Heigl quit and Isaiah Washington was forced to apologise and seek counselling after verbally attacking gay co-star T.R. Knight in between takes.
Pompeo eventually decided enough was enough and she recruited show creator Shonda Rhimes to help her make production on the series a more fun, positive experience for cast and crew alike.
"After Season 10, we had some big shifts in front of the camera, behind the camera," she added. "It became my goal to have an experience there that I could be happy and proud about, because we had so much turmoil for 10 years."
"My mission became, 'This can't be fantastic to the public and a disaster behind the scenes.' Shonda Rhimes and I decided to rewrite the ending of this story. That's what's kept me (here)."
Motherhood also played a big part in Pompeo's choice to take action - and stay with the show.
"Once I started having kids, it became no longer about me," she said. "I need to provide for my family. At 40 years old, where am I ever going to get this kind of money? I need to take care of my kids," she shared.
Pomeo has three children with husband Chris Ivery.
Currently the highest-paid woman in dramatic television, Pompeo was also out to prove the show could still be successful after star Patrick Dempsey left the series in 2015.
"Patrick Dempsey left the show in Season 11, and the studio and network believed the show could not go on without the male lead," she added. "So I had a mission to prove that it could. I was on a double mission."