If Roman culture had been a continuous force in Europe, that might be said. However, after the Germanic invasions, Europe went right back to the Iron Age level of civilization that had existed before Rome invaded. The Roman language, literature, architecture, political system, and the like had a greater impact on Europe during the Renaissance than it did under Roman occupation. Petrarch did more to Romanize modern Europe than did Caesar.
I wouldn't disagree with this point, MPC, only to add that especially in the case of literature and other areas, the people of the Middle Ages and Renaissance often viewed the times of the Greeks and Romans with much romanticism (sorry about that) in discussing the glory days gone by.
Nevertheless, there were stronger efforts to 're-introduce' Latin, both in the Church and in educated circles. Between the advancing education of the peoples--they had more books at their disposal, and could understand them better--and the advances in technology in all areas--where often Latinized names were used--there were more 'educated' words coming into the system. For example, many of the 3-syllable words in Spanish, particularly those with ante-penultimate stress, come from re-introduced Latin words in the Renaissance period.