Those power supplies are constant voltage.
When there was no current limiting used with that power supply, the leds will get ruined.
As stated on the page of the leds, they need to be driven with a current of 350 mA.
You could use your existing supply if you place a current-limiting resistor in series with the LEDs.
The choice of resistor value is determined by the desired current (eg. 75% of the maximum spec of the LED), the number of LEDs in series (each has a Vf spec), and the voltage of the supply. The power rating of the resistor should be at least double the expected dissipation, calculated as I^2*R or ∆V*I.