Ms Yates stood with Charlie's father Chris Gard to praise Charlie.
The couple wept as she told the High Court: "So sorry that we couldn't save you."
"Our son is an absolute warrior and we could not be prouder of him and we will miss him terribly," Ms Yates told the court.
Click here for the full statement by Connie Yates that was read to the High Court"One little boy has brought the world together and whatever people's opinions are, no one can deny the impact our beautiful son has had on the world and his legacy will never ever die.
"Charlie has had a greater impact on and touched more people in this world in his 11 months than many people do in a lifetime.
"We could not have more love and pride for our beautiful boy.
"His body, heart and soul may soon be gone, but his spirit will live on for eternity and he will make a difference to people's lives for years to come.
"As his mum and dad, we will make sure of that. We owe that to our boy.
"We will do our utmost to ensure that no parents have to go through what we have been through and the next Charlie that comes along will get this medicine before it's too late and Charlie will save many more lives in the future, no doubt about that.
"We are struggling to find any comfort or peace with all this, but one thing that does give us the slightest bit of comfort, is that we truly believe that Charlie may have been too special for this cruel world.
Charlie Gard's parents end legal fight for life after new medical reports"We truly believe that any parent would have wanted the same thing if they knew what we knew.
"We are now going to spend our last precious moments with our son Charlie, who unfortunately won't make his first birthday in just under two weeks' time."
She added: "Mummy and Daddy love you so much, Charlie, we always have and we always will and we are so sorry that we couldn't save you.
"We had the chance but we weren't allowed to give you that chance."
Ms Yates said the last 11 months had been the "best" and the "worst" of times.
"The last 11 nearly 12 months have been the best, the worst and ultimately life changing months of our lives but Charlie is Charlie and we wouldn't change him for the world," she said.
"All our efforts have been for him.
"This is one of the hardest things that we will ever have to say and we are about to do the hardest thing that we'll ever have to do which is to let our beautiful little Charlie go."
She added: "Put simply, this is about a sweet, gorgeous, innocent little boy who was born with a rare disease, who had a real, genuine chance at life and a family who love him so very dearly and that's why we fought so hard for him."
Ms Yates said a new scan had forced a change of heart.
"We are truly devastated to say that following the most recent MRI scan of Charlie's muscles ... as Charlie's devoted and loving parents we have decided that it's no longer in Charlie's best interests to pursue treatment and we will let our son go and be with the angels."