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Lists of endangered animals only include beetles and butterflies if they bother to mention insects at all. Here is an example from where I live:
http://www.dec.ny.gov/animals/7494.html
All of the insects are beetles, dragonflies, moths, butterflies and there is a mayfly, but that is kind of similar to a butterfly when it comes to their "fanbases." Where are the ants, lice, silverfish and aphids? Is there a better list?
I am not aware of a better list, but you are right that (1) many insects have gone extinct recently, and (2) documentation of insect extinction is poor. An article in Conservation Biology (2005) says
The biodiversity crisis is undeniably an insect biodiversity crisis. Yet insect conservation remains the awkward “kid sister” to vertebrate conservation. Nowhere is this clearer than in what we know, or rather do not know, about insect extinction, particularly for those extinctions that may have already occurred. ... What accounts for the tens of thousands of expected but undocumented insect extinctions? What does this discrepancy mean? How important is it to our understanding of extinction and the future of ecosystems? These should be questions at the heart of species conservation, yet they have hardly been addressed. No peer-reviewed articles have been published reviewing modern insect extinctions, and no estimates of global extinction rates have explicitly focused on insects.
--Modern Insect Extinctions, the Neglected Majority (my emphases)
The book Insect Conservation Biology (2012) may have more info, though it still seems to focus heavily on the more charismatic species like butterflies.
Lots of insects are considered threatened and endangered. The global IUCN Red List (International Union for Conservation of Nature), which is arguably the most important tool for evaluating species' threats globally, is listing 1382 insects as threatened (categories: Near threatened, vulnerable, endangered, criticaly endangered and extinct) and this includes a wide variety of taxa. A large number of taxa have also been evaluated as 'data deficient', which means that they might be threatened, but we do not have enought information to say. Overall, global assessments have only been done for a small proportion of all insects. However, there are also regional (country) IUCN red lists which include a much larger range of taxa.
The knowledge level differs widely between countries though, which means that some countries have hardly evaluated any insects at all while others have relatively good information. In Sweden (which I'm most familiar with), we have a comparatively good overview of insects, probably due to a long tradition of natural history. For instance, species counts on the Swedish Red List includes 196 Hymenoptera, 855 Coleoptera, 217 Diptera, 67 Hemiptera, 545 Lepidoptera, which represents 27%, 19%, 13%, 7% and 21% of all species found in these groups in Sweden. In Cerambycidae (Longhorn beetles), which I've worked with, about 45% of all species are currently red listed.
Generally, the knowledge level on species trends over time or occurrence patterns is limited in insects though, which can make the evaluations difficult. The red list includes 5 main criteria, and indirect data (e.g. amount of broad habitat classes) are often used as proxies for species abundances or potential number of subpopulations. The process of actually determining a species as extinct is difficult though (not only for insects), since rare insects are often found very seldomly. Some "naturally" rare species might be found as singletons with several years between each occurrence, and the cut-off for considering a species as extinct can then be hard to define (a long period of no occurrences could just be a sampling issue). The situation is made easier if there is a clear trend from relatively high abundances trending towards extinction.
