Unless your referring to the notion of us actually helping to establish Israel in the first place, then yes this is our fault for sure.
Stupid Greatest Generation, thanks for getting us into this mess.
In all seriousness though, let's remember what happened here. Israel withdrew from Lebanese territory because the UN promised to help the Lebanese government control the area and maintain the border. The UN instead did what it does best...nothing and Hezbollah, that terrorist organization responsible for the deaths of hundreds of Americans you may have heard of it, was allowed to gain control of southern Lebanon. In the meantime, our friends the Iranians, who have publicly called for the destruction of a sovereign state, armed Hez. with tens of thousands of rockets and drones. As Bush would say, "Heckuva job, UN".
Hez. then crosses an international border and murders (I say murder because terrorists are not members of nation's military and therefore are civilians who murder other people) Israeli soldiers and kidnaps two more. Israel then attacks Hez. in response. Innocent Lebanese citizens are killed because the Lebanese govt. has allowed Hez. to become entrenched within their civilian population and the terrorist group hides their weapons in population centers, ensuring high civilian casualties in the hopes that the international community will concentrate on this loss of innocent life rather than the initial terrorism that sparked the incident. That strategy is successful.
One month later, a toothless cease fire is agreed upon. Hez. is not destroyed. Iran is not even mentioned in the UN resolution though there is no question that the Iranian govt. is responsible for the actions of Hez. Hez. claims a great victory and retains the ability to further terrorize our Israeli allies. Much like Clinton's failed Middle East "peace" accords, this resolution ensures there will be more violence in the future.