The migrant crisis is often attributed to the Syrian Civil War; how was the Syrian Civil War "caused by inadequate US foreign policy in the Middle East"?
The refugee crisis is not just Syrian, it's also very much Afghan and Iraqi. I think the main mistake has been to consistently prioritize opposing Russia over fighting Islamism and a failure of working more eloquently towards a peaceful solution for the Palestinians.
A number of socialist leaning, authoritarian but secular regimes, all cold war allies of Russia, were removed with the help of the US and the UK (Afghanistan, Iraq, Libya), leaving behind chaos and civil war. Assad was the last of the bunch and he was very nearly toppled with US help before the Russians saved his ass.
I have no sympathies for these regimes and dictators, but not realizing even after multiple failures that they were not the worst that could possibly happen in those societies was a terrible mistake.
Continental Europe is bearing the brunt and the fascist right in the US and the UK are pouring scorn over the EU for failing to sort this mess out, even exploiting it to support their claim that anything other than bigoted nationalism of the Trump and Brexit variety is bound to fail. "Told you so!"
There was a lot of opportunity for the US to put an end to Assad, with a lot more credibility then elsewhere in the Middle East, but that was decided more by the US people's reluctance to get into another war.
The result would probably have been as messy as Iraq was initially, but probably not as messy as what is there now.