Yes, he did, and it was fundamental to his entire economic philosophy: https://en.wikipedia.org/wiki/Tendency_of_the_rate_of_profit...
but one of the core ideas of marx's conception of history is that human needs, wants, and human nature itself are constantly in a state of change and that those needs and desires are in large part a product of the environment in which you live, and further that humans and human society in turn change their own environments which in turn change human nature itself
Interesting, though, that per the very same article someone like Adam Smith concurred empirically with Marx's observation on the titular tendency of rates of profit to fall. This suggests to me it likely had some meat to it.
Basically dude thought the competition inherent in capitalism would cause all profit to be competed to zero leading to an eventual 'crisis' and collapse of the capitalist means of production.
Implicit in this assumption is the idea that the things humans need and want changes/evolves in a predictable way, and not in a chaotic/fractal/reflexive way (which is what actually happens).
An eventual static basket of desired goods would be the only mechanism by which competition ever could compete profits to zero. If the basket is dynamic/reflexive/evolving, there's constantly new gaps opening between human desires and market offerings to arbitrage for profit. You can just look at the average profit margins of S&P500 companies over time to see they are not falling.
The further we get from subsistence worries (Adam Smith's invisible hand has pulled virtually the entire globe out of living in the dirt), the more divergent and higher abstraction these wants and needs become, and hence the profit opportunities are only increasing -- which is how the economy grows (no, it's not a fixed pie, another Marxian fallacy).