You will hear a clicking sound as the A/T arm switch on the MCP goes from ARM to OFF and a red flashing A/T discrete light in front of both pilots.
Really? I'd have thought the 737-800 would be like the 747-400, in which case an autothrottle disconnect will set off a warning beeper, and give an EICAS AUTOTHROTTLE caution message. The autothrottle switch on the MCP will just sit where it was...in ARM.