Are we to blame for Mexico's war?

Yes, and no. It is true that the USA is the target market for illegal drugs. We have been fighting a war on drugs that is a farce for decades. They have invaded our schools, devestated many carreers and families, and undermine our social fabric. The war though is a farce! Government has used it as an excuse to expand and invade our private lives. It has enlarged our court and prison systems as well, and there is no incentive to win it or end it. It is an excuse to feed bottomless thugocracy.

I have never used drugs, and I hold users in low regard. I would not support the war on drugs. I regard it as a personal choice, and it has personal consequences for the users. If that was the only thing, I would say live and let live. BUT since those users feed their habit by stealing from me and other hard working folks, blight neighborhoods and communities, and endanger the health of all Americans, I want to see it won.
The drug trade has devestated Mexico. Gangs, cartels, rule much of the country. They kidnap and rob as well. If they stuck to just carting drugs, Mexico would not be in the predicament it is now. Cartel members have waged a war for several years now. It has expanded in scope to where they are murdering workers from our consulate whom they think are helping rival gangs.
Some blame the USA for this violence and say we are culpable. I disagree. We are at war too. Gang violence on the streets of many of our cities is tied to the drug trade. the bloods and crips are a prime example. They have spread from the streets of LA to a neighborhood near you.
We need to change our tactics at home. Drug dealers need to be executed. Ones who sell to children or use children in their service need to be executed in a most horrible manner. I would opt for feeding them slowly through a grinder, or dismembering them alive in the neighborhood where they plied ther trade.
We need to cut the crap! Build the border fence. That is the first step in winning the war, cut the supply lines. There are several benefits to this. It cuts down on the area we need to monitor for drug traffic. It eliminates the cheapest route into the country. It drives the drug trade off shore. This will help Mexico because it will draw the cartels out of the interior. Since we will be able to observe traffic on the ocean far easier then traffic over land, enforcement will become easier as well. I have seen video of drug boats attacked by Coast Guard choppers. They do a darn good job. treat them like an invading army. No trial, no quarter, sink their boats, and strafe the survivors in the water. better yet, bomb the survivors with pots of fish guts and blood, draw the sharks to a feeding frenzy.
If they fly the drugs in, shoot down the aircraft. REQUIRE every aircraft crossing the border to have a prepass. They must enter at a designated time, fly a designated route, and land and be inspected by customs. Planes that stray get blown away. We need aircraft like the Douglass Skyraider for the mission. A plane that can pace a Cessna or Leerjet, and can handle abuse.
The gangs are willing to kill to get the drugs here. Until we are willing to kill to stop them. we will not win.