Nugent's clinical finish brought him an eighth goal of the season in the 17th minute, while Vardy raced through and rounded goalkeeper Ryan Allsop to restore the Foxes' lead in the 64th minute.
But Leicester dominated the second half and Bournemouth's cause was not helped when Ward was sent off for a second bookable offence in the 66th minute, after fouling Danny Drinkwater.
Howe said: "I thought in the first half we were well in the game and had some really nice passages of play and a couple of good opportunities where we didn't really work the goalkeeper.
"We conceded a goal and showed good character to not let that affect us and scored a great goal ourselves.
"At half-time you think it could go either way. But in the second half I don't think we quite hit the level we did in the first half and it was backs to the wall.
"We were coping okay but conceded a poor goal and the sending off changes the game from our perspective. It was very difficult to build any pressure.
"We felt we had weathered the storm, defended set plays very well and hung in there.
"We felt that the longer we could keep it at 1-1 we would have a great chance to win the game.
"But that spell with the goal and the sending-off knocked us because you struggle to keep the ball with 10 men. I have no complaints about the sending-off. I think they were both yellow cards.
"But I think we can take encouragement from our performances in the two games against Forest and Leicester."
- Sports & Recreation
- Jamie Vardy