In Star Wars: Episode I - The Phantom Menace we see the Galactic Republic, the society in which Obi-Wan was raised and trained. We see the grand Temple of the Jedi Order on Coruscant, where generations of Jedi live, meet, and train, the Senate that governs the Republic, and evidence of a safe, inclusive, and prosperous civilization. Even Naboo, a remote planet subject to a blockade and invasion, is clean, safe, and fairly well-off.
In stark contrast we are shown the world of Tatooine, which is outside the jurisdiction of the Republic, where there is visible poverty, slavery is accepted, and crime and random violence, or at least threats of violence, is unremarkable.
In a fairly short period of time the Republic and its society falls apart, with the Clone Wars erupting and leading to the collapse of the Republic and the rise of the Empire. (The Empire being militaristic, human-chauvinistic, and repressive.) In parallel, there is the destruction of the Jedi Order, starting with Order 66, and continuing with the Purge.
So Obi-Wan was born and trained in a period of relative peace and prosperity, only to survive the destruction of everything he was trained to value and protect. The "more civilized time" is the era they did not know was ending when he and Qui-Gon were dispatched to Naboo.
You can even take his previous comment:
Not as clumsy or as random as a blaster.
as a direct commentary on this as well; blasters - in sufficient quantity - being responsible for the deaths of a great many of his fellow Jedi.