They went in at the break leading 9-6 and the introduction of England internationals Martin Corry and George Chuter in the second half inspired them to a win that takes them five points clear at the top of the table.
Howard admitted: "We didn't touch the ball for the first 35 minutes.
"The passion wasn't a problem and we defended well, but we were getting done on the set-piece.
"It was important to see if the players could dig themselves out of the hole and we dealt with the personnel when we realised that they couldn't.
"Once we got the ball we were dangerous. Geordan Murphy made some inroads, but we had to play off scraps for most of the first half.
"But if we hadn't given away so many silly penalties, we would have been further clear."
Harlequins director of rugby Dean Richards saw his side claim a losing bonus point thanks to a last-minute penalty from Andrew Jarvis that took his personal haul to 17 points.
England winger David Strettle was replaced in the second half, but Richards revealed his injury was "just a bump on the leg".
Richards added: "We missed a few opportunities in the first half, but we would have been happy with taking a point from Leicester at the start of the season.
"We came here with nothing to lose and came away with a point. We have to be happy with that and we might have had more if we had taken our chances.
"The boys have had a few disruptions with injuries in the last couple of weeks, but I have confidence in my players and they worked extremely hard."