This issue is covered in detail in "Cathedral, Forge and Water Wheel" by Gies.

Yes, Western Europe lagged behind China and the Caliphates from about 600 - 1000, maybe even 1100. We know of a lot of technology that was known to Roman civilzation, but lost to WE during this time - e.g.: tree grafting, road construction and cement. Others were just poorly used, if known, like windmills which seem to be curiously ignored until about 800 ... there are many examples.

Other items were known in China or India but not WE - wheelbarrows, the chain pump, the suspension bridge, certain smelting techniques, cotton production and of course paper (including TP). Money also significantly disappeared in Western Europe during this time. Some greek works only exist today because they were translated into Arabic, the original Greek is lost.

The Caliphates were in pretty good shape until the Mongols mostly destroyed Baghdad.

Round about 900 - 1100 WE populations grew, and significant innovation started to make itself felt, but there was slow innovation throughout this period.