This is more of an engineering question. They would have been too heavy with just a slight amount of armour.

Germany's biggest airships, the R-Class Zeppelins had a length of 198m and a radius of 23,8m. For brevity's sake, I'll calculate their surface as a hollow tube with equal measurements. It'll be a bit off, but the problem will become readily apparent;

The whole "tube" would have a surface area of 14866m^2. A 1 mm steel plate has a weight of 7.85kg/m^2. If we were to cover the whole tube in 1mm steel, we'd end up with 116 tons of steel.

The unarmoured Zeppelin had an unladen weight of 36 tons and an added 27 tons for crew, fuel, armament etc... so, even if we cut our steel tube in half (because we want to only armour the belly), we almost double the zeppelin's weight. We would also have to strengthen the internal structure to account for the added weight, which will drive our weight up even further - we'll get into diminishing returns really fast.

All of that for a 1 mm steel plating, which will perform just a little bit better than cardboard under fire.