I'm not completely up to speed on the distant past of the EU so somebody feel free to correct any mistake in the following statement, but Yoda became a Jedi at the start of what was considered a lengthy period of relative peace and prosperity in the Galactic Republic, arriving on Coruscant to begin his training not that long after the last known Sith went into hiding and were believed to have gone extinct. Memories of the most recent battles between the Jedi and the Sith were still fresh in the minds of some of the older members of the Order who were alive at that time.
For roughly eight centuries the Jedi's combat and weapon skills were used to counter and combat criminals and relatively low-intensity conflicts and skirmishes that would occasionally arise on Republic planets, and the Battle of Naboo of 32 BBY followed by the Clone Wars ten to thirteen years later marked the first major armed conflict of any kind to happen in the Republic in many centuries. Obi-Wan's "more civilized age" comment in ANH was meant to refer to most of Jedi history though certainly not all of it. It was a general statement.