Not typed on a B737, but why was the auto throttle system disconnected at the same time as the AP at minimums? Can you not have the ATs working for you on the B737 with its AP off?
Jet Jockey A4, it is Boeing SOP to disconnect the auto throttle when the autopilot is disconnected, which is the procedure most operators seem to use. However, some operators use a slightly different procedure, in that 'speed' mode is deselected on the MCP & the auto throttle remains armed.