My Application allows only one user to login/perform any operation at a time but jmeter is able to do the same process/request multiple times without throwing any error using same user credential simultaneously. I've used record and play function of Jmeter and it is able to do the same request multiple times without throwing any error. I have used multiple users in my thread group that's why it is doing same request multiple time but this should be shown in red or fail as my application support that one user can be used only once to perform any operation.
If I understand your issue correctly, you wonder why JMeter is not showing fail request in red color for multiple users, Right?
No, this is not how JMeter works, actually red color/failed request is shown only when your application throws error or JMeter didn't get any valid response. In your case your application has restriction that one user can login only at one time and not from multiple machines at same time. But when you run script using JMeter with same user multiple times, your application still passes a valid response to JMeter (like 'User already logged In' or 'Not able to login' or most of the times 'Application throws user back to login page') and that's why you get a normal sequence in results and not the red color. This is how JMeter works, it doesn't care about the expected response and if you analyze the results you will see that users other than first user has not actually been able to login.
So, if you use a 'Tree Listener' and navigate to the request which you expected to be in Red, and open the "Response Data" tab, then you will see the HTML response of the request sent and received by JMeter, this response will tell you what actually has happened and you might be able to see that any user other than the First one is not able to Login i.e. for other users you will either see the Login page or Validation message.
Now, you need to understand the difference in Expected and Valid Response.
Expected Response: is the response you are expecting and you want JMeter to validate the same too and then show a Pass/Fail request on the basis of the expected response vs. actual response. You can do this using Assertions and in your case you should use it just to see the difference. You can use the 'Response Assertion' for validate the response i.e. Homepage is shown or not.
Valid Response: is a non-error response which JMeter has received from the application it can be Expected one or non-expected one.