As with all questions of "what did the Vikings think about X," we have to start with sources, or more accurately, our near-complete lack thereof. We have no narrative sources written by Viking-Age Norse people; our saga sources come several centuries after raiding fell out of practice. Basically everything we've got is from early medieval England and Francia, the victims of the raiding. They portray the Vikings as this horrible scourge and a punishment from God, though not an undefeatable one. The vita of St. Edmund (a king of East Anglia who was killed in 871 by Vikings) claim that they were drunkards, rowdy and immoderate, and eager for violence; Edmund was killed when the Vikings drunkenly decided to use him as target practice for spear throwing.

Not every English source is so negative. The Battle of Maldon puts this speech into the mouth of a Viking: " Seamen sent me quickly to you,
ordered me tell you to send rings at once,
wealth for defense: better for all of you
that you with tribute this spear-rush forgo
than that we share so bitter a war.
Nor need we kill each other if you perform it;
for gold we will fasten a truce with you.
If you determine it, the mightiest here,
that you for your people ransom will pay –
give to the seamen at their own choosing
wealth for a truce and take peace from us –
we with that payment shall to our ships,
on ocean fare, hold peace with you.”

This doesn't tell us much about the raiders' mentality; paying tribute, or fighting to avoid paying tribute, is very well-attested through all the Old English sources. However, the Vikings do not seem particularly eager to go into battle either, another thing that is definitely borne out by the chronicles (people eager for battle tend to not be routed easily, and the Vikings are defeated and flee somewhat regularly in the annals).

Now, we aren't totally reliant on Old English texts to tell us about the Vikings! we have contemporary written texts in the form of runestones, we have some Viking-Age poems preserved in younger manuscripts, and we have later sagas telling stories about the Viking Age.

Turning to our Scandinavian sources, such as they are, we do see fragments of information in non-narrative contemporary sources or later sources that mean we're not completely high and dry on their mentality. Most runestones are commemorative, being raised as tribute to a family member who died. A whole class of these deal with expeditions to the eastern Baltic, called "Gardarike stones." They're cataloged at Uppsala University here, alongside most other rune texts. Now, many of these indicate that there was raiding in the Baltic, and dying out there was sad, but worthy of memory. It wasn't something that needed justifying, or was perceived as awful. And in fact, going on such a raid was honorable enough that some of the deceased were honored with quite expensive carved stones! Additionally, alongside these stones, related stories were told, an excellent way of being preserved in memory, and some of these stories eventually morphed into Yngvars saga viðförla, according to Lars Lönnroth (Lönnroth, Lars, 2014. "From history to myth : the Ingvar stones and Yngvars saga viðförla" In Nordic Mythologies: interpretations, intersectionism and institutions*.* edited by Timothy R. Tangherlini. Berkeley: North Pinehurst Press).

In the sagas, one cultural aspect that becomes clear that likely bears continuity with the Viking Age is the importance of honor. Being well-regarded in the community was important, and could be done by wisdom, by generosity with material wealth, or by courage. Raiding was one way to earn wealth and regard, often in service of the king of Norway. Too many sagas to list have raids at least mentioned, but Egils saga and Njals saga are probably two of the best-known sagas and both have a section where characters (often the sons of the lead character) go off raiding. So, at least by the 1200s, raiding was regarded as something appropriate for these heroes to do.

The same three traits persistently get praised in the first part of Hávamál (a long poem in the Poetic Edda, whose first part is a glorified advice column). So, we can extrapolate that back, especially since at least part of Hávamál existed in the 10th century, that honor was measured in the same terms. Raiding and distinguishing yourself in courage on a raid was a good way to win honor and wealth, which could be given away. Therefore, it wasn't something to be justified; they simply did not see it as murder. And, if you died, then you would be commemorated and that is also honorable.

The poem Hákonarmál, which appears in the 13th century Heimskringla, but is attributed to the 10th century poet Eyvindr skáldaspillir, is a praise elegy for the (Christian) Hákon the Good. Although he was Christian, he was buried as a pagan and in the poem, he is greeted with great praise in Valhalla.
The second to last stanza again speaks of the importance of memory in honor:

Góðu dœgri verðr sá gramr of borinn,
es sér getr slíkan sefa,
hans aldar mun æ vesa
at góðu getit.

Poetry is a pain to translate, but it reads something like:

"it becomes a good day when that kind of king is born
who gets for himself such affection.
It will always be [said] of his age/reign
that it received a good thing"

By doing good things in life, he is commemorated in death, and his honor outlives him. (The same ethos is really clear in Beowulf's dying speech, by the way).

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TL;DR Our sources are not great for how the Vikings justified their raiding, but it seems that they did not view it as something bad that needed rationalizing to begin with! Instead, it was something that was eminently practical, both for wealth and for honor. If they could do that without violence, they were happy to take that deal, and if not, courage in battle would ensure that they were commemorated, which was an important social virtue.