"felt exasperated" is correct and can be used in written English.
You can use it to express a feeling of extreme annoyance and frustration. For example, "As the same mistake kept happening over and over again, I felt exasperated with the lack of improvement."
Looking at it, I constantly felt exasperated.
I felt exasperated with them because I felt people should – in the days when people didn't really get divorced – at least put up a show of getting on in front of their child".
Not long after that, during a session where my wife expressed tearful frustration and we both felt exasperated that our attempts at play therapy seemed so futile, the same counselor made a suggestion: "You need to let yourselves grieve".
I have also felt exasperated as the bookseller, with his Dickensian surname, turns into a litigant out of Jarndyce and Jarndyce, still refusing to sell the portrait for any money.
Another protester, disturbed both by the violence in Charlottesville and the president's reactions to it, felt exasperated that Trump would continue to harp on divisive messages.
They may also feel exasperated.
Certainly many Chinese scholars and, presumably, officials feel exasperated with North Korea and rather embarrassed by its antics.
On the other hand, the older generation feels exasperated by its inability to take advantage of what seems to us huge pluses.
It's wonderful to read about such an intelligent heroine, you never feel exasperated towards her for being naïve for example.
When I think about Salinger in his later years — literally half of his life — I feel exasperated by this withholding and the elevation of silence into the highest virtue.
