Connacht were beaten 20-9 by Conor O'Shea's side, having failed to convert a large amount of pressure and possession into points in a hard-fought round 3 encounter.
Elwood, who is in his first European campaign as the province's head coach, said: "I'm getting quite fed up with saying we're playing a nice brand of rugby. At the end of the day, we're in the business of winning rugby matches.
"Even though we're doing a lot of good stuff, it's not winning us games and it's actually costing us points.
"Particularly in the second half, we had an abundance of ball to cause them problems. I think we did cause them problems and we had line-breaks and offloads and so on and so on, but we just didn't have that killer punch to finish things off.
"It's frustrating because it's another week where we're creating opportunities but we're not putting teams away.
"We're playing a nice brand of rugby but I wouldn't mind winning ugly now and then as well. That's the frustrating part: that we have to work so hard to create our opportunities and get our scores and then you see that, in my view, Harlequins got two soft tries.
"They might see it as a bit of brilliance from their players but they're a soft 14 points as far as I'm concerned. That's us chasing the game," he added, referring to the scores from Tom Guest and Mike Brown.
After a promising start to the season, recent results have not quite gone Connacht's way. They have been on the wrong end of a number of tight scorelines, but Elwood knows that one win could make all the difference when it comes to regaining that early momentum.
"Losing can become a habit and winning can become a habit. The sooner we get over the line in a couple of close games then the belief might be there that we can do this week in, week out," he added.
"But when you start to drop off in games over the last few weeks, the guys might doubt themselves. We try to keep the guys confident, tell them to keep believing in what they're doing and believing that it's right.
"But the guys have to live that and do it on the pitch and then they get the belief from that also.
"We have a lot of young players and it's part of their development. At least we're competitive every game this season. We're going to stick by our guns because we actually believe that the stuff we're doing is right.
"I'd like to be winning more than we're losing but I've got to stay positive and keep instilling the belief in the lads that what we're doing is correct.
"It knocks the stuffing out of you on nights like Sunday but we have to stay positive. Hopefully we'll turn the corner sooner rather than later."
Tickets for Friday's much-anticipated match are available to purchase here.