As you mentioned, a small flat screwdriver works best.
However, you can use basically anything that's thin, stiff, and non-round.
I used to do this all the time to my brother to piss him off (ah, youth).
Some of the things I've used: The metal clip from a cheap pen
A paperclip with the very tip bent to a 90 degree angle (to simulate a screwdriver)
A safety pin (bent like above).
Works a bit better, due to stiffer metal.
The end of an old tangled up Slinky (bent straight) A metal coat hanger with the tip hammered flat Creativity goes a long way here.
lifehacks.stackexchange.com/users/89/TIO Begs
The flat end of a cheap teaspoon.
Not all types work though, more expensive teaspoons often have fancier handles that won't work.
It's stronger then most other methods using paperclips or other improvised things
and you don't have to hammer anything flat.
If you don't care about the spoon you can bend it in the middle for extra leverage.
lifehacks.stackexchange.com/users/1600/Pieter B
If there is a round hole in the middle of the door knob, push a carpenter nail into the hole, dead-center and push against the spring.
The lock will release, as if magic.
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2.5 inch nail works everytime in my experience.
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Bobby Pin or even Safety pin will work too.
If you don't have either open your wallet and take out an old laminated card.
Insert it between the door and the door frame about where the lock cross bar goes into the door jam.
If the curved part is facing you place the flat edge of the card sung against the curved lock bar and pull the door knob towards you as you are pushing the card snug.
The door will open.
If the curved lock bar is facing away from you use the corner of the card to tickle the top or bottom back edge of the lock cross bar.
This might mean bending the card slightly.
Again you are trying to release the lock bar by applying pressure on the curved edge that goes into the door jam.
After a few seconds when you feel the corner edge of the card is snug against the lock cross beam, again apply pressure to the doorknob pushing it away from you and pulling it towards you as you press on the card.
After you get the card in the right spot when you pull the door towards you you should feel the cross bar give and the door will swing open.
This also works for outside door locks with more substantial locks.
Just not deadbolts.
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I have an interior door with a twist lock. It locks from the inside and on the outside takes this type of key:

However, I lost the key, and seem to have locked the door before my last exit. What can I use to access the room without damaging the lock?

Note: my precision screwdriver set is locked inside this very room.
How to open a privacy lock doorknob without the key?
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<substitute-tool><locks><hardware>
lifehacks.stackexchange.com/questions/5471
lifehacks.stackexchange.com/users/15/Mooseman
There are a number of ways of opening a privacy lock doorknob without a key. You could try using a small flat screwdriver, the flat end of a teaspoon or a laminated card. Similarly, a bent safety pin or paperclip may also work. It may also be the case that there is a round hole in the middle of the door knob, and if you push a carpenter nail into the hole, the lock will release. The options are to release the spring using thin and stiff such as a paper clip, safety pin or coat hanger, or open the latch using a credit card.
Anything thin, stiff and round will do, such as a paper clip or a safety pin or a coat hanger. Try the flat end of a teaspoon. If there's a round hole in the doorknob push a nail in to release the spring. Use a credit card to open the latch.