I contributed to IRA after filing return for 2023.Do i need to file 1040-X along with 8606 to report the IRA contribution as non-deductible ? Or only 8606 form is enough?

The proper way to file Form 8606 is attached to Form 1040-X.
Form 8606 can be mailed by itself only when you are otherwise not required to file a tax return.

Did you do a true backdoor contribution that is tax-free?
in that case Form 8606 will show a taxable amount of zero.
Do you have the correct taxable amount on Form 1040 Line 4b and did not take a deduction? (Schedule 1 Line 20)?
If that is all true then only Form 8606 has to be attached.
After you e-File,
get Form 1040-X from IRS website and mail it in with your 8606, which you can also get in fillable PDF.
Note: when you are not changing any dollar amounts on your amending 1040-X, you can leave all the lines 1-23 EMPTY.

Part III explanation: "didn't include Form 8606 with e-File".
You will have to mail it so this does not use up your one 1040-X e-File.
Done this way, you sign 1040-X, not 8606.
Do not include your old 1040 nor your revised 1040 because the Form 1040-X reflects any changes there and becomes your new tax return.

@narkhsa1