I would like to clarify something. Under international law, only the Security Council has the right to authorize the use of force. NATO cannot legitimately act alone.
The problem with the Libya mission is that, at the Security Council, Russia and China abstained on the resolution authorizing the use of force. They were disappointed, so to speak, with the way the mission was conducted and with the fact that they lack political control and influence over NATO actions. This is the root of the current problem with Syria. They do not want a repeat of what Moscow and Beijing see as the mistake, the failure in Libya.