Donkey work usually means work which is primarily repetitive and/or intellectually undemanding, sometimes with the implication that muscle power is the worker's primary contribution. The archetypal example, of course, being a donkey walking in circles all day turning a millstone. If the donkey actually thought about it, he might well resent never getting anywhere. Luckily, he's only a donkey, so he doesn't think like that. And the miller is perfectly happy so long as his corn gets ground. Common alternatives are scut work and grunt work.
It's important to note that the above expressions don't particularly imply inefficiency. Any given speaker might like to imagine he could use his brains to figure out a more efficient way of doing things, but that's just a natural consequence of the fact that most people don't like boring jobs, and many people think they could organise existing work practices better than their current boss.
Inefficient working practices arise from many possible causes. For example, in British English we speak of Spanish practices where a workforce over-prioritise their own (often, short-term) interests at the expense of efficiency (often, by retaining concessions which are no longer appropriate). In other contexts, a method might be described as roundabout if it's not the most direct way of doing things, or brute force if it relies more on muscle/computer power than on a specific carefully-designed approach.