Charlotte Charles told reporters: “Job done, promise complete.”
Sacoolas, a former employee of the US intelligence services, did not travel to London for the hearing after Washington said it “could place significant US interests at risk”.
Mr Dunn was killed when Sacoolas drove her Volvo on the wrong side of the road outside US military base RAF Croughton in Northamptonshire on 27 August 2019.
His family have since endured a three-year legal battle.
Ms Charles said their campaign was now “properly, properly complete.”
“Anne Sacoolas now has a criminal record for the rest of her life. That was something she never thought she’d see. The US government never thought she’d see and we worked tirelessly and relentlessly to make sure she still had to do what you and I would have had to have done.”
“Yep, Harry, we’ve done it. We would have been happy with anything ... for us, it was just about doing the right thing.”
Ms Charles called Sacoolas a “huge coward” for not attending the sentencing.
With her voice breaking, she said: “She should have been there. We would have been. I think it’s despicable that she didn’t come over on the judge’s orders. Huge, huge coward.”
She said the family of the teenager had the option to leave justice hanging and choose not to pursue the case.
“We weren’t cowards,” she continued. “We didn’t back down because we have values. Maybe she doesn’t.”
In court, Ms Charles wept as she said: “I didn’t make it to the hospital in time before he passed and the thought of that haunts me to my core. My job is to comfort my children and I wasn’t there for Harry to comfort him in what must have been an awful and painful, slow death.
“Harry just disappeared out of my life that night, shattering my existence forever.
“His passing haunts me every minute of every day and I’m not sure how I’m ever going to get over it.
“I made a promise to Harry in the hospital that we would get him justice and a mother never breaks a promise to her son.”
Sacoolas’s lawyer Ben Cooper KC told the court that she is deeply remorseful for what has happened.
Mr Cooper read a statement on her behalf, which said: “I am deeply sorry for the pain that I have caused and it is for that reason that I have been committed to a resolution of this case. I know there is nothing I can say to change what has happened.
“I cannot imagine the loss and I too deeply grieve for Harry and his family.”
Max Hill KC, director of public prosecutions, said: “We have today seen the end of the journey to secure justice for the family of Harry Dunn.
“Many thought we’d never get to this point – but I hope it sends a clear message that we are steadfast in our commitment to bring people to justice.
“Despite the challenges that arose as the case progressed, our expert prosecutors were able to secure a guilty plea and Sacoolas has now been sentenced for causing the death of Harry Dunn.
“Harry Dunn’s family has shown immense strength and bravery throughout the long road to get to this point in the proceedings. Having met them, I know that their determination to secure justice has never wavered.
“Neither has ours.”
Additional reporting by Press Association