Let's calculate the difference between supplies to see how much power they both deliver:
The formula for power is:
Power (Watts) = Current (Amperes) * Voltage (Volts) or
P = I * V
Original power supply:
P = 3.25 A * 20 V = 65 W (as indicated)
The new power supply:
P = 3.42 A * 19 V = 64.98 W (with significant digits this rounds to 65 W)
So both power supplies deliver the same power.
The issue is around whether there is enough voltage delivered or too much current delivered. Each electrical component in the computer needs a certain voltage. When you add these all up, your total voltage should be less than the voltage delivered by the power supply. In your case you're providing the laptop with less voltage than it used to receive from its old adapter (and more current).
When the engineer originally designed this laptop they would have selected a power supply that provided more voltage than the laptop needed to provide some tolerance and depending on how easy they wanted to make it for the consumer to modify or expand the devices in the laptop, they may have selected a power supply that delivers even more voltage than the stock laptop needs (this is common with desktop power supplies).
The question you have to ask is how much tolerance was built into this solution -- can you get away with providing 1 volt less (keep in mind at this scale we're talking about a 5% difference which can be significant)? Maybe. Maybe not. I don't know and I can't tell you. The engineer could have selected a power supply that delivers exactly the voltage needed. You won't know for sure unless you can measure it.
Depending on the laptop model you have you can likely pick up a replacement power supply. And here's the kicker, you'll find that the replacement may be a different part and in some cases it is also shared with other models from the same manufacturer. It is possible that it provides different voltage and amperes than your original (I have seen this several times with Dell). In this case the manufacturer knows the device and the power it needs and can make the decision as to whether the power supply is suitable for your model. It might be worth looking into what the replacement supply's specs are and seeing how they compare to your "junk" adapter.