It is very difficult to know about the mental processes of death of common people in Mesoamerica because not a lot of historical sources describe how they felt. Unfortunately, it isn't like most people were keeping diaries or writing letters to one another back then that can be collected and read today.

It is even more difficult to know for sure because historical sources do not say nearly as much about ritual killings as you might think based on how central we now imagine sacrifice to be to Mesoamerican society. Most of the historical footing for ritual executions comes from Spanish friars who greatly exaggerated the practice with very little cultural knowledge about why it happened, let alone any sensitivity or tact that might help modern people understand the practice more fully. They certainly never interviewed families of victims to see how they felt. They definitely did not ask if everyone in Mesoamerica over the centuries thought that these ritual practices were acceptable because they were so holy and important to the functioning of the universe, or if they were terrible abominations. The frairs' goal was to condemn the Aztecs and the Mayas, and justify why conquering sovereign peoples was ok. Sadly, now human sacrifice is really the only thing that people know about Mesoamerica. Unfortunately, everyone seems to think that the Aztecs and the Mayas were terribly bloodthirsty monsters...barely even human. Go on any reddit thread that mentions the Aztecs outside of AskHistorians and just wallow in the macabre fascination of the Aztecs' supposed barbarism. It's really horrible how much this myth sticks around.

But of course the Mayas and the Aztecs mourned their dead because they cared for the living. Camilla Townsend has a great passage about this in her book Fifth Sun on page 51, which she bases on Nahuatl sources. She explains that the Aztecs knew that the world was dangerous and that if they lost their wars or their fortunes in the world changed that many would lose their lives to their enemies. "Mothers taught their children that the world was a dangerous place. 'On earth we live, we travel, along a mountain peak. Over here is an abyss, over there is an abyss. If you go this way, or that way, you fall in. Only in the middle do we go, do we live.'" She goes on to explain that "mothers valued their children dearly, more than anything else in life---they said that they were precious, like polished gems, or iridescent feathers, treasures fit for high kings." Mesoamerican societies also had a tradition of being brave and stoic in the face of death. There was great honor and holiness in death in war, in captivity, and being executed for the deities in order to keep the world going. The ceremonies were not bloodcurdling orgies of violence, but sacred moments.

In Central Mexico, people believed that soldiers and sacrifice victims went to a special afterlife place in the land of the dead. Bernardino de Sahagun, drawing from Nahua knowledge at his school established shortly after the Spanish invasion, provides a description of three places where people went in the afterlife that he learned about from his Nahua helpers. There was the afterlife journey that people who died of natural causes went on after death. There was the watery afterlife for those selected by the rain gold Tlaloc. Sacrifice victims went to the land of the sun, along with soldiers killed in battle. Women who died in childbirth also went there, showing how a woman's battlefield was perhaps with the dangers of childbearing. People in the land of the sun later transformed into birds, especially hummingbirds, which were powerful symbols in Mesoamerican cultures. These details are overviewed in Elizabeth Baquedano's chapter called "Concepts of Death and Afterlife in Central Mexico," which you can find on her academia page if it is of interest for you. I would also add that this just one source of information. It is very likely based on the variety of funerary practices that have been uncovered archaeologically that there was likely a vast multitude of other beliefs about death and the afterlife, not just in Central Mexico but also in Mesoamerica.

Most people, however, were not sacrificed because most of the people who died that way...not all...but most...were prisoners of war, were men, and were elite. Ritual executions were rare events. But obviously most people were normal people, humble farmers, business people, and craftspeople, who died in other ways. They knew that death was a part of life, and the speeches and funerary practices all reminded the living that they too would have an inevitable death. Some of the few Nahuatl sources that survive are poems and songs that mourned the loss of loved ones, and praised them for their bravery or lamented their misfortune. They were songs of love and really quite beautiful. The humanity of these creations, the care they showed the dead from all stations and walks of life, the rituals the practiced when someone died, and the important goods they left for them show that yes, death was a normal part of life but also that the individual would be greatly missed here in the land of the living.