If the Europeans were so much better, why didn't the Americans import some experts

The famous Italian general Giuseppe Garibaldi was offered a commission as Major General in the Union army. He turned it down because (depending on who you talked to) he wanted to be the Commander-in-Chief of the entire Union army, or Lincoln was unwilling to explicitly state the end of slavery as a war aim.

Regarding the "nation of immigrants" comment, at least one foreign born person was giving a general's commission and placed in charge of foreign born volunteer units(Carl Schurz). Although he had been an American citizen for many years at that point, rather than a expert contracted for the job.

EDIT: You could add Franz Sigel to that second paragraph as well. And he had graduated from a European military academy, but didn't perform particularly better than other Union generals.

Did US commanders know they were getting criticized during the war?

Yes, of course. But here's something that many, many people fail to recognize:

The Confederacy was not performing a whole lot better. Indeed, throughout the war the Union was advancing everywhere, with the "problem child" being the area between DC and Richmond. So, it's hard to make a compelling argument that the practices of most the Union army were so bad that they needed outside help to fix them.

The Union leadership certainly felt as if the Army of the Potomac was being poorly run compared to elsewhere, hence the revolving door of COs and bringing in successful generals from other theaters to "fix" the problem, some more successful than others.

Firstly, I think it should be said that the superiority of European tactics and military organization in the 1860s is not universally acknowledged by historians. In fact, Brent Nosworthy has suggested tactical differences in the American Civil War may have resulted from a higher standard of marksmanship by American recruits rather than any contemporary difference in tactics.

But largely American Civil War officers were actually trying to adapt up to date European tactics to the American local conditions. There was no secret that Europeans knew and American officers had yet to learn, rather it was a question of adaptation. European militaries had large peacetime establishments, conscription plans, and known opponents. The American Civil War was fought suddenly, without prior military planning or infrastructure, and across massive distances, while amidst political turmoil. This scale of multi-faceted improvisation was incredibly different, and a few Europeans who knew how to conduct a cavalry charge or handle artillery would have made little difference. Franz Siegel for example was an experienced german General officer who was mostly ineffective either as a subordinate or in an independant role in the American Civil War.

Source: Nosworthy, Brent "The Bloody Crucible of Courage: Fighting Methods and Combat Experience of the Civil War"

Can you post the other write-ups? They sound interesting.

Follow up quesitons:

Can someone refer me to those earlier write ups? I don't have a formal background in Civil War history, but my impression is that despite some incompetency the Civil War actually led to a lot of battlefield innovations. IIRC the Ken Burns documentary mentioned that the war began like the Franco-Prussian War, but progressed to a proto-WWI situation near the end with features like trench warfare, rapid fire weapons like the gatling gun, etc. Is that true? I'd especially like to know in reference to naval combat, for which I'm almost certain the ironclads (and tactics developed in using them) represented the cutting edge.