Pools took the lead after just 58 seconds when Marlon Harewood set them on their way with a close-range header from Jack Barmby's corner.
Pools added a classy second when midfielder Bradley Walker curled home a beautiful shot from 25 yards and number three arrived after 56 minutes from Simon Walton's penalty before Jon Franks rounded it off in the 90th minute from 12 yards.
Rovers never troubled Pools goalkeeper Scott Flinders, except for an 85th-minute strike from Chris Beardsley which crashed against the crossbar.
Ward's side sit four points from safety, but face an anxious few weeks ahead.
"No complaints, absolutely not," Ward said. "I'm quite embarrassed by it.
"It's a long time since I've felt this way, certainly not in the 14/15 months I've been here.
"We went under a little bit tamely, not something we have ever done before - we have always fought it out and been hard to beat, but not here.
"We have been beaten by a good team, don't get me wrong - Hartlepool are a very good team and played very well.
"They have some very good players, but we have assisted with their goal effort and chances, but at the same time they have taken them."
Ward, whose side have won just once away from home this season, added: "We are all embarrassed by it.
"We conceded after a minute from a set-piece, something we talked about before the game.
"The best laid plans of mice and men....
"Their second goal was a fantastic strike, and you put your hands up and say well done.
"We were still around the game at this point, but made catastrophic errors to concede the third and fourth goals."