I bought a machine from the US last week with 110V specifications and used a step down converter for use in Pakistan which has 220V specifications. When plugged in and turned on, there was a pop sound followed by a burning smell and some smoke. Does this mean circuit damage or power board damage? Should i send it back to Nespresso or will a local electrician be able to take care of it?

It sounds like something blew in a big way. Likely to be the main power supply board. The step down transformer should have reduced it to the 110 volts you require. Check the transformer to make sure it does actually reduce from 220 to 110 vac. Also check the hertz , (hz) ( cycles) Australia uses 50 hz at 240 volts ac. im unsure what hz USA or Pakistan is. Confirm your transformer output meets the electrical specification of the coffee machine. There may be a local Nespresso machine repairer who will convert yoru USA spec machine to Pakistan voltage thus negating the need for a transformer. It may be a bit expensive replacing all the electrical comonents though, it may still be worthwhile.