Having a filtration system doesn't mean it's a good idea to create more pollution. In the same way that having a washing machine doesn't mean it's a good idea to start deficating in your pants.
Simple, get a miniature nuclear reactor to power the recycling of CO2 into O2 and C. You can then electrolize H2O to get more O and combine the H2 with the C from earlier to make gas for the generator.
Yeah it only gets to be a problem when you have to change the filters. Otherwise any apocalypse that involves a significant loss of atmospheric oxygen or major change in composition ain't something you can wait out, you gotta evolve past that.