Economics did play a huge part in the decline of the Roman Empire. However, your understanding of it is not entirely correct.

For one, the economic issues of the Roman Empire stretched far before the reign of Diocletian. This is where I get to talk about the problem of inflation and currency debasement. So the roman denarius was the standard roman currency for much of the empire and had generally maintained a steadily declining amount of silver in each coin during the Early Roman Empire. Under Augustus, the denarius was 95% silver while under Trajan, over a century later, the denarius only declined to 85% silver. Fairly good so far right? Then came Caracalla and the 3rd Century Crisis. Caracalla was famous (or infamous) for lavishing his soldiers with donatives and pay raises. As his father Septimius Severus purportedly said, "Be harmonious, enrich the soldiers, scorn everybody else". But where to get all the coins? Well, to produce more coins, why not just lower the amount of silver in each one? And so under Caracalla, the percent silver of each denarius decreased to a bare 50%. While this did give a short-term boost of funds for the emperor, it had horrible longterm consequences. When Caracalla was assassinated, bringing about the period known as the 3rd Century Crisis, successive emperors would debase the coinage so that by 268 AD, the denarius was a scant .5% silver.

So what were the effects of this? A decline in commerce was one. Commerce grounded to a halt not just because of the military instability of the empire. Since no one could rely on the roman currency to retain value, the economy reverted to a much more localized barter system. The next effect was an incredibly oppressive tax system. With regular coins no longer having any significant value and emperors having larger and larger military expenses, gold was the standard form of tax payment. But if you were a poor farmer, you couldn't afford gold. As the empire declined, you would see a huge amount of land just being abandoned. The people who didn't abandon their lands were increasingly forced to sell their land and work under local lords. This would eventually contribute to the feudal system that would dominate the medieval age. Finally, you have the increase in localism, which could be seen as a combination of the first two problems. With decreased commerce, the different areas of the empire were less connected. As local lords gained power, the central governmental apparatus declined. As the empire declined, you will see that the emperors would hold less and less influence as the people looked to local rulers instead of the Roman government.

Now to talk about Diocletian. Diocletian did introduce a much more burdensome government apparatus. However, he repeatedly tried to fight inflation by either standardizing old currency to a set amount of precious metals or introducing new currencies. He had very limited success with this, as inflation would continue under his reign and after. What is more, he also introduced a much more standardized and efficient taxation system. Before him, emperors would frequently rely on simple seizure of goods to pay for their expenses. Under Diocletian, a census taken regularly with taxes being assessed by the value of labor or land. While the tax rate was still high, it was predictable. Though his policies were draconian, they were also fair and I personally believe that his economic reforms, taken in total, aided the empire and delayed its collapse.

Sources:

Inflation and the Fall of the Roman Empire by Joseph R. Peden

A Companion to the Roman Empire by Nigel Pollard

Roman Empire by Nigel Rodgers