Don't stop current animation to play next animation

I'm trying to create a combat system where 1 animation plays then if the player hits the attack button while the animation is playing the next animation in the sequence will play. My problem is that if I hit the attack button it will immediately stop the current animation and play the next animation. Is there a way to stop the second animation from playing until the first animation is done? I tried to mess with queued but that didn't quite work, maybe I was doing it wrong. Any help would be great!

 

Are you using mechanim with an animation state machine? If so, just make sure the transition has 'Exit Time' enabled, and then set an Exit Time late enough in the clip. This will make it so the original animation has to reach the specified exit time before it can transition out.