You need to find the details of this tax, i.e. when it was enacted and when it was to start being assessed. In all honesty, it's not clear in the letter when that happened. You really need to nail this down, because honestly the landlord MIGHT just be covering himself now after the fact and passing the shit downhill to you. Or he might be getting screwed just as much as you (hit by a stupid city tax that they are making retroactive, which would be really lame).
I would think that if you resigned a lease after April 2011 and he knew about the tax and didn't include it, that's on him and not you, and you don't owe him a dime. I don't know that to be the case though. If it is a brand new tax, and the city government is actually making it retroactive almost two years, then I think you're just SOL.
There's a few details missing in here though, and honestly you'd need to dive into the tax itself to find out the specific timeline. I wouldn't hold anyone at fault just yet. But personally, I wouldn't take the letter from him lightly, although you do need to do your research too before you just hand over $1050 in "back taxes."
EDIT: Just read your post above. IMO, the landlord's ignorance isn't your problem. If he "didn't know" then it's on him to pay up for the retroactive taxes. But then again, if you put up a fight you might find yourself without a place to park your car pretty fast. It's really up to you. I don't think you should owe him anything though.
'11 BMW E92 ///M3 - ZCP and DCT
'13 Toyota Tundra - 4x4 Platinum CrewMax, 5.7l iForce V8