Recently i have found that in one of the Cisco WS-C2960S-48FPS-L switches in our environment, portfast enabled to a interface whichis connected to a non-managable switch.
But 3 servers are conencted to that non-managable switch.
Since this switch is connected to only servers, there wont be any problem, right??
I see two aspects to this issue: first, whether it will work correctly in your network exactly as-is, and second, how will it react to several what-if scenarios.
In your current network in the precise state it is now, with that unmanaged switch having a single uplink to the managed upstream switch, and having a number of non-looped links to devices that do not perform Layer2 switching/bridging among themselves, using the PortFast does not create any issues.
If we start thinking about what-if scenarios (what if another uplink is connected to the upstream switch, what if somebody connects a cable and inadvertently or deliberately creates a physical loop, what if the servers are interconnected and configured with some sort of bridging), certainly, the PortFast is absolutely inappropriate as it will allow at least transient switching loops to occur, and it is not clear if the managed switches will have enough CPU power to recover from the loop after it starts flooding frames all over the network.
So I would personally put it this way: It is not a recommended scenario, and it is not a best practice approach. Then again, in a tightly controlled environment, it is just like any other powerful tool that either helps you make things work better, or will come back haunting you if used improperly. It is up to you to decide if the benefits outweigh the risks involved. In any case, having an unmanaged switch alone is a risk enough.
This reminds me strongly of how we were told strongly on my classes of programming not to use the GOTO command. Sure, it allows all kinds of bad things to do. However, there are certain situations where a judicious usage of GOTO command simplifies the resulting code complexity and memory footprint significantly. You could find the GOTO statement used quite often in Linux kernel code, for example - and surely, Linux kernel coders are by no means lamers in C programming. It is simply about knowing exactly what advantages, disadvantages and risks does it involve to use such powerful mechanism. The PortFast towards a single unmanaged switch is, in my opinion, quite a similar story.