A concentrate/extract cartridge for dispensing a liquid concentrate/extract is provided. The cartridge includes a hollow body and a dispensing tube that contains a pumping device. The cartridge includes a valve having a valve stem that passes through a port of a valve seat connected to the dispensing tube. A piston is located at a first end of the valve stem and a valve body is located at a second end of the valve stem in removable contact with the valve seat for alternately opening and closing the port. The piston can also includes a membrane positioned on a side facing the valve stem configured to permit a flow of fluid into the dispensing tube when the valve body is in contact with the valve seat and to permit the fluid to be forcibly expressed from the dispensing tube when the valve body is moved from its contact position. A liquid dispenser suitable for numerous applications, having a removably insertable concentrate/extract cartridge and a method of dispensing a liquid are also provided.