This is actually a quite tricky question. Of course you must specify which culture and types of innovations you are referring to.

For western and European culture there is of course the fact that much of the technology and knowledge of the Romans was practically lost after their decline: cement, elevators, road building etc. This doesn't mean however, that between 1000 and 1500 nothing was invented that wouldn't shape our society today - quite the contrary.

Just a few examples:

The banking system we have today evolved in 14th century Italy (with predecessors in such institutions like the Knights Templar). That's why many terms are still of Italian origin: credit, solvent, brutto, netto, cheque - the word bank itself derives from the banca, the bench where the moneylender would sit. You could get credit or receive a sheet of paper to exchange for your money at another place after a trip or so

The idea of self governance through a council - of course people love to refer this to ancient Greek democracy, and that's where the enlightenment derived it from - but the idea that certain urban elites could vote for their own government was practiced in the medieval cities of Europe for centuries, without any ideological base

Architecture experienced a few remarkable changes in the middle ages as well. Think of the changes from the Romanesque style (small windows, sturdy walls) to the Gothic style (large windows, pillars and arches bear the weight) - that's mastery of statics!

Maybe less positive: Gunpowder and the cannon. These didn't revolutionize warfare until the invention of the Arcebuse, but cannons were already used by the English in the 100-Years-War. They proved burdensome in battle, but quite effective in sieges

Universities: teaching the people of high birth and/or high skills in certain fields raised the intellectual level of Europe significantly. They codified ancient Roman law (Bologna, the oldest University and first with a law school) and invented Scholasticism. Although not necessarily a modern school of thought this approach to philosophy and theology - ultimately truth - reintroduced the idea of logic and rational thought

Paper: Although an imported idea from China, the Europeans figured out how to make it themselves with their own resources.

Printing Press: The mother of all media revolutions started when Johannes Gensfleisch (aka Gutenberg) invented a printing press with movable letters. Literacy skyrocketed, When before a manuscript of the bible was worth half a village, a printed version became available even for a wealthy burgher.

I could go on and on - but remember that even if you say the discovery of the Americas started modernity, the Santa Maria was built in the middle ages (I'm not a big fan of strict limits between the eras)