Newcastle manager Eddie Howe admitted the same afterwards.
Branthwaite said: "The best save I've ever seen, I don't know how he's pulled it off.
"We know how much of a top goalkeeper he is. When he does things like that it's magic, he's kept us in the game at the end of the day."
Howe also stated: "I've got to say that’s one of the best saves I’ve seen live. I thought it was outstanding.
"I think when you put it in context of the timing of the game and what it meant, obviously a frustrating one for us."
Everton boss David Moyes also said: "I was laughing. I was going to run on the pitch and celebrate a save again.
"Sandro Tonali couldn't have hit that any better, it was technically brilliant but the save was out of this world.
"Jordan played well today, helped us out a lot and his save was top notch."