From the point of view of the new job, it's good that leaving your old position isn't a reflection of your work. But I'm not sure it's worth bringing up. Is the new role in the same industry? If so, your old place struggling and you needing work, could put you in a weaker position regarding...
It may depend on the type of work you're doing, but I'm not sure there's any benefit in telling them.
Also, why were you let go (rhetorical)? Is the answer something that would put your prospective employers off you?