Capture exit status from function in shell script

You need to use return instead of exit inside the function:

_EXECUTE_METHOD () { return 1; }

_EXECUTE_METHOD || echo "Got error"

exit will terminate your current shell. If you have to use exit then put this function in a script or sub shell like this:

declare -fx _EXECUTE_METHOD
_EXECUTE_METHOD () { exit 1; }

_EXECUTE_METHOD || echo "Got error"

(..) will execute the function in a sub-shell hence exit will only terminate the sub-shell.