Faramir's statement is nearly identical to a paragraph in the Silmarillion, in the Akallabeth, which is the story of the rise and fall of Numenor in the second age of Middle Earth. They were Aragorn's ancestors, who were granted extended life spans and a swanky island for their valiant efforts in the wars of the first age. It's a long story, but basically they all descended from Elrond's brother, so Aragorn is Elrond's nephew, several hundred generations removed...

Anyway, the people of Numenor, despite living several hundred years and having a sweet island and all kinds of technology, are disenchanted because they don't live forever, like the elves. Sauron shows up and exploits those feelings, driving them to ruin.

What happened in Gondor was just an echo of the path their ancestors took.

So, was Tolkien anti-science? Not surprisingly, much has been written on this very topic. Most of these discussions focus on the corruption of the Shire during the war of the ring, the smoke stacks and the mill and the fouling of the Brandywine River. Claims are made that this represents the experiences of Tolkien's childhood and his experience during WWI.

However, Tolkien's world is full of technologic achievements. Feanor, especially, who created the Simarils and the palantir, is famous not only for his skill but his arrogance, which lead to his, and many other's, tragic ends.

The elves forged the rings of power in a kick-ass display of technology, but since Sauron was their consultant, things went wrong.

I think that Tolkien's view of science and technology (or magic) was that it can be used for good or evil. When tech followed and enhanced nature, that was fine. But when it was used to change what was ordained, trouble ensued. What got the people of Numenor in trouble was that despite having very long lives, they still died. Death was the natural order, actually described as a gift from God. But that wasn't good enough for them, they wanted the eternal sadness of the elves.