With the shutdown in place, many people were out of their jobs for the duration of the shutdown. This means that they weren't spending their money on things besides the bare necessities and it also means that there weren't people utilizing the services they worked for, which likely also hurt the economy.
For every dollar that the government spends, the private sector is deprived of spending that dollar. If there was a government shutdown (which really doesn't exist, since there are so many "essential" departments"), then the dollars that would have been spent by the government would be spent by the private sector. Private spending is more efficient than government spending, so a government shutdown would actually help the economy.