This is an exceedingly broad question. Probably hundreds of companies were involved in Disneyland's "construction." But I think you really need to define what you mean by "construction."
For example, do you mean who leveled the ground? Who removed/relocated the trees? Who designed the buildings (say, on Main Street)? What firms constructed those buildings? Who built the rides? Who built the ride components?
Just to give an example with which I am familiar, look at the steam locomotives on the DRR: Dixon Boiler Works build the boilers; Wilmington Iron Works built the frames and wheels, and everything was put together by Disney. Lots of the parts used on the passenger cars came from Lovsted, a company in Seattle.
There are so many companies/people involved that it may be impossible to note everyone. Bill Evans did the landscaping. As I recall, he wasn't yet a Disney employee--just an outside contractor like the rest. Many of the attractions were built by outside companies--and some weren't even built specifically for Disney--like the Dentzel carousel.
The Mark Twain was built by Disney, but Dixon supplied the boiler.
Looking through old phtos, we may be able to ascertain who built specific attractions and structures.
But first, I think we need a better understanding of what you mean when you ask who "constructed" Disneyland.