I am looking for academic works prove or state that the US or EU encountered problems in fighting COVID-19 because of balancing liberty of civilizations.
The causality you assert is stated in somewhat odd terms, so I doubt you'll find a quality academic paper to discuss it like that.
In general, personal reluctance or downright opposition to Covid-fighting measures translates into two things: personal non-adoption of such measures and possibly public protests as well. (Note that personal non-adoption is already a "problem" in the sense that it reduces the effectiveness of the measures.)
Now protests can cause a policy to be rolled back or ended prematurely, but it's fairly hard to prove causality in that regard... in an academic setting. (In punditry, it's a different matter.) And that's because there are alternative explanations possible for why a policy was changed like "the government was worried about the economic impact of the measures" (and of course the latter, i.e. economic impact, correlates to some extent with votes and protests.)
Now to save this answer from being just an extended comment, there's at lead one paper that correlates the level of democracy with the anti-Covid measures adopted. And they
postulate[s] that the quality of democracy explains the variation of COVID-19 responses across democratic countries, i.e. the higher the democratic quality the lower the restriction of individual freedoms and the concentration of power on the national executive.
They do this by analyzing the response (alas) just during the 1st wave of Covid-19 in Europe. In essence they correlated two measures of restrictions (the Oxford COVID-19 Government Response Tracker (OxCGRT) index and the Pandemic Backsliding (PanDem) data from V-Dem) with the Zurich Democracy Barometer main measure and some of the sub-indices. Here's just one the regression graphs they produced (using a dependent variable just the OxCGRT index):
In the conclusion section, they relate their finds with a couple of other papers:
Countries that are more dedicated to individual liberties continue to do so even in moments of emergency. Our study thus not only buttresses the findings by Sebhatu et al. (2020: 2) that ‘stronger democracies are slower to react on the face of the pandemic’, but adds to further understanding this finding by pointing out the reluctance of vertically and horizontally accountable decision-makers to adopt public health interventions that encroach on civil liberties. Furthermore, our paper strengthens earlier findings on ‘pandemic backsliding’ (Lührmann et al. 2020): in countries that already experienced democratic backsliding, the pandemic opened up a window of opportunity for power-seeking leaders to further concentrate power.
I would add that this data needs to be taken with a grain of salt, because in some dictatorships like Belarus, the leadership decided that Covid is no problem.