Since technology is a pretty general term with different tools and techniques developing at different rates the best way to answer the question would be on a case-by-case basis.

To take a good example that's been in the news recently, one could point to the sophistication of the antikythera mechanism. The intricate mechanical workings of this device exhibits a level of craftsmanship and scientific understanding that wasn't repeated until after the European Renaissance, which is pretty long time indeed.

Or we could look at Romanesque architecture that developed in the immediate centuries following the collapse. Romanesque architecture is identifiable as bearing some of the typical hallmarks of classical architecture but lacking the engineering know-how to implement structures of equal sophistication. Consequently we find buildings that employ columns for example almost haphazardly with consideration given to their aesthetics rather than to their function as load-bearing. It wasn't until the gothic era when architecture became technically impressive in its own original way. Individuals with mathematical proficiency just weren't around in enough numbers until that point.

I'm sure someone who studies this sort of thing specifically could provide insight into more practical, everyday technologies related to farming, construction, and other day to day actions and I'd be really interested to hear about it.

As it was already correctly stated, technology is a broad term. Some aspects of it suffered more than others. Not to mention I find it difficulty to talk about science before the scientific revolution.

What I can talk about is civil engineering, and in that area there was a decline and it was a huge one. The romans were likely the best engineers that had been up untill that time. Their use of the arch, vaults, domes and concrete made possible for them to create structures of a level of sophistication that was not seen before, like the Colosseum, the Pantheon, the Baths of Caracalla or the Basilica of Maxentius to name a few.

After the fall of Rome in the west, structures of this scale and complexity are nowhere to be seen. One exception was the Palace of Aachen in Germany built by Charlemagne. But it was still far from pushing the boundries set by the romans. That began to change with in the 11th century and finally Europe matched, and maybe surpassed roman engineering with the rise of the great Gothic Cathedrals (a far descendent from late roman basilicas) in the 12th and 13th centuries. By the 14th century it is safe to say west europe was building structures that were impossible in roman times, like the Florence's Cathedral.

But that's structural engineering, there is also the aspect of infrastructure in which the romans were also very good at. They built roads, many of them paved, all across the empire. They built bridges, aqueducts, sewers, planned towns, canals, ports. And these kinds of buildings, more than techinical knowledge, requires a strong government that can afford to build them and see it as an advantage. They require long term planning. So even if west europe could built those, they weren't doing it in the scale of the Roman Empire. For example, it's likely thtat a system of transportation as effective as the romans roads didn't exist in Britain untill the railroads of the industrial revolution. So I'd say the europens didn't complete surpass roman infrastructure as a whole well into the industrial revolution, but were slowing catching up in this area or that for centuries before.

In short: Structural engineering: matched and surpassed between 12th and 14th centuries. Infrastructure: matched and surpassed in different areas throughout the 10th and 19th centuries.

It is really hard if not impossible to quantify technological progress, so I'm afraid no one will be able to come up with an answer, no matter how vague it is.