Share your schematic now. You will need a couple 0.1uF capacitors (ceramic are best for this use) attached directly to the Vcc pin of both chips, and grounded on the other leg of the cap. Do a site search for "decoupling capacitor".
CR2032 cells are good for 1mA or maybe 2mA, that might be something you don't realise.You need to decouple each logic IC with 100nF on each supply pin to ground, and maybe22 to 47uF electrolytic somewhere on the supply for good measure.
How are you clocking the ATtiny?
Your battery symbol is drawn backward. The longer bar is positive:
...But still want to know that, is it need a capacitor for this project?