Light switch doesn't turn off lights
STOP!!!!
You have messed things up. Sorry to be blunt. But electricity is dangerous, so this is really a big deal.
Safety First
Turn off the breaker for this circuit. NOW! What you have described might be fairly benign, but you might have caused some parts of your electrical system to be &quot;hot&quot; that should not be.
Assuming you are in the US (if you are not, please say where you are as different countries have different color codes):

Neutral is white or gray and only needed on a switch if it has &quot;smarts&quot; of some sort (timer, dimmer, WiFi controls, etc.)
All other colors (except green/bare == ground, which you have handled correctly) are HOT or SWITCHED HOT.

Your new switch has a neutral connection? That implies it is something more than &quot;just a switch&quot;. Not a dimmer (since you said so), but is it a &quot;smart switch&quot;? A timer? Something else special? In any case, the red wire is not neutral and should not be connected to neutral on the switch. If you actually need neutral then you need to find neutral - typically a bundle of white wires stuffed in the back of the box, but sometimes not in the switch box at all because old construction did not require neutral in the box.
Old switch: &quot;2 black wires going into copper leads&quot; - what does that mean? Was it two black wires connected together onto one wire or screw? If so, they likely need to be connected together to the &quot;in&quot; connection on the new switch. If they were two separate connections on the old switch then this is impossible to guess, but a 3 way switch is a possibility.
Pictures
A picture is worth a thousand words. Please upload pictures of the old switch (preferably showing model # if you can), the new switch (again showing model # if you can), and the switch box showing all wires as clearly as you can.