Anything can be done in virtually any language.
That said there is a level of practicality. As your system's complexity increases, you need better tools to manage it.
The problems are still solvable, but you start to need more people and much more effort in design. I'm not saying other languages don't benefit from design, I'm saying that the same level and attention to detail may not be required.
Since we programmers are Human (I am at least) we have troubles in one area or another. My biggest is memory. If I can visualize my code as objects, manipulating large modules in my head becomes easier, and my brain can handle larger projects.
Of course, it's even possible to write good OO code in C, the patterns were developed in C by manually managing dispatch tables (tables of pointers with some pointers updated to point to different methods), and this is true of all programming constructs from higher languages--they can be done in any language, but...
If you were to implement objects in C, every single class you wrote would have a large amount of boilerplate overhead. If you made some form of exception handling, you would expose more boilerplate.
Higher level languages abstract this boilerplate out of your code and into the system, simplifying what you have to think about and debug (a dispatch table in C could take a lot of debugging, but in C++ it isn't going to fail because the code generated by a working compiler is going to be bug-free and hidden, you never see it).
I guess I'd say that's the biggest (only?) difference between low level and higher level languages, how much boilerplate do you hide. In the latest batch of dynamic languages, they are really into hiding loop constructs within the language, so more things look like:
directory.forEachFile(print file.name); // Not any real language
In C, even if you isolated part of the looping inside a function, setting up the function pointers and stuff would still take lines of un-obvious code that is not solving part of your primary problem.