Uh ... no?
Look, where do you get your food from? The local grocery store. Where do they get the food from? For some (not a lot) of it, local farms; most of them come from companies that move the food from where it's grown to either where it's going to be consumed (for fresh food) or to where it'll be processed (canned, packaged, slaughtered, whatever), thence to transshipment locations, typically ports or trainyards, thence to warehouses and distribution centers, thence to the stores. Most food isn't grown five miles away from where it'll be eaten any more. Food needs to be moved, and so that requires fuel. No surprise, fuel needs to be moved, from where it's acquired (mined for coal or uranium, pumped for oil), to where it'll be processed/refined, thence to where it'll be used - whether that's a power plant or a gas station.
All this 'movement' requires a truly exquisite amount of cooperation; merchants during the pre-Industrial era would be amazed, even stunned, at the amount of movement of goods undertaken and considered normal these days. However, that cooperation relies on the people who cooperate feeling safe with those with whom they're cooperating. If you have a justifiable fear of the guy who sells you, say, beets, then you're going to be reluctant to deal with him - whether that's because you're afraid he's going to bite you as he turns into a zombie, sneeze at you because of VITAS III, or rob and kill you because you have money and are buying two whole tons worth of beets from him. Exchange 'beets' for anything else - sugar, clean water, medicine, gasoline, or whatever catches your fancy - and the problem remains the same. The issue is essentially identical if the modes of transportation (whether that's a port, a railyard, the trains, the oil pipeline, or lots of ships) are destroyed, except instead of 'won't', you have 'can't'.
It gets worse. Your needs stay the same while the supply - both the local and the shipped supply - dwindles. When the 'what we got in the cupboards' runs out in 3 or 5 days, people risk going out into the street to get food from the market. When that runs out in a week - because people aren't shipping it, because the guys in the Port of New Orleans no longer trust the guys on the ship from Bahrain or where-ever else - then you have people raiding each other, robbing houses for food, heading out to local farms to raid them, etc. Some coastal people will turn to piracy; despite modern concerns about piracy, if you compare tonnage shipped to tonnage arrived, we have a truly miniscule level of it in today's world. Change that up, add in the fact that there are going to be bandits too - people will turn bandit in a heartbeat in order to get their hands on a food shipment if they're starving and (worse) they're watching their kids starve - and it just keeps going downhill. Soon enough, it reaches the tipping point where it becomes much, much harder to turn the situation around; problem is, that point is usually reached before those in charge realize it.
Going off the standard pre-mechanized-farming ruler, it required 7 farmers to feed themselves and 3 town-dwellers - 7 farmers per 10 people, typically within 10-20 miles of the town or city (because you still have to move things, but now it's by horse). As the fuel stops flowing (because most people don't live within 10 miles of an oil field and cracking plant), you have to return to pre-mechanized farming methods. Me, I live in Atlanta; there are something like 7 million people here. There are not, trust me, (7 million / 3 = 2.667 million * 7 =) 16.33 million farmers within, oh, a 50 mile radius of the 50-mile radius that is Metro Atlanta.
So, within weeks, Atlanta dies, and dies horribly, because gas and diesel won't get here, so food can't get here.
Repeat across continents.
Edit: Or, y'know, what farothel says so succinctly. And yeah, I didn't even include 'natural' diseases from the corpses stacking up ...