If that is all, the short answer is: “you are close but, no, you do not have a private cloud”. Let me explain:
You see, the premise of cloud services is the high degree of automation using underlying technologies that make intelligent decisions on behalf of the IT Pro to maximize availability and leverage existing resources. This level of automation is characterized by being scalable, highly available, self-healing, and ITIL compliant computing.
Virtualization is the very first step. You have a private cloud when you are 1) virtualized and 2) have all the system management components in place to achieve the level of automation needed. Item #1 is self-explanatory. Item #2 involves a) having a monitoring solution in place (i.e. SCOM) that will detect that there is an issue (i.e. certain workload is causing high server utilization); b) Process automation component (i.e. Opalis) that is the brain and decides what to do; c) Change management system (i.e. SCSM) that opens/closes a ticket/change request; d) Configuration management component (i.e. SCCM) that carries out the corrective action; and e) Virtual machine manager (i.e. SCVMM) that can span new VMs should the corrective action call for it -- I have used examples of Microsoft management products to ease the example if you are familiar with the SC stack but it does not all have to be MS products.
So, you see. From problem detection, to decision, to tracking, to remediation – all while are we may be sleeping; and it is all documented and can be reported on. This is what makes the cloud so powerful leveraging technologies to carry out what would have otherwise had to be manual. This helps an organization achieves agility, optimum resource utilization, agility, business continuity, high availability, scalability, and elasticity. This is not all talk. This is available today.