Appointed in midweek, Hughes saw his side, bottom of League One, ripped apart with three goals in eight second-half minutes.
After a lively start in which Coventry goalkeeper Joe Murphy saved well twice from Ryan Noble and then Jon Franks, Pools offered nothing.
Carl Baker opened the floodgates after 51 minutes. His low shot from 20 yards went in off the inside of the post and six minutes later it was 2-0 when Peter Hartley handled in the penalty area and David McGoldrick rolled in from 12 yards.
The quick-fire third came when Baker, with his back to goal, flicked the ball into space and effortlessly volleyed home from 10 yards.
Frank Moussa got the fourth after 75 minutes. Pools lost possession on the edge of the area and, from a lighting-fast counter-attack, the midfielder took a possession to curl home and substitute Adam Barton was only on the pitch for a minute before smashing in from 16 yards.