"It was a big night defensively and there were a number of positives to come out of it, but it doesn't help having to make changes to the defensive pattern when you have a man in the sin-bin."
The westerners had stand-in captain Frank Murphy and prop Ronan Loughney yellow carded during the game in Llanelli, and Elwood knows his side cannot afford further indiscipline at Firhill Stadium on Friday.
"Discipline is an issue, we've spoken to Frank (Murphy) and Ronan (Loughney) and to the rest of the squad to discuss the four yellows in two games. It is hard enough competing with fifteen players never mind losing two."
Connacht have certainly made a high-scoring start to their league campaign, tallying up 73 points and seven tries in their opening encounters with the Newport Gwent Dragons and the Scarlets.
Elwood added: "The team have really bought into it (the brand of rugby), the players know their roles and we are trying to play with a bit more ball in hand.
"I don't think we made the wrong decisions last Saturday, we empowered the players to make those decisions on the pitch and it is paying off."
Connacht's flying winger Fionn Carr, who scored a hat-trick of tries last Saturday, is seeing the benefits of the new regime.
"We've worked on integrating the forwards and backs and we shown what we can do when we keep the ball alive," he said.
"The players work together and we have a good sense of what each of us are trying to do."
Meanwhile, Elwood is under no illusions as to how tough this weekend's match against the Warriors is going to be.
"Glasgow are fighters, they are battlers. They are a very physical side. They have a good set of forwards and they compete very heavily at the breakdown," he explained.
"They work very hard in their defense. They are very committed. We won't get anything easy over there.
"It is always a very tough place to go. We will be looking forward to a 'roll your sleeves up' type of affair!"
To watch highlights of Connacht's game against the Scarlets, click here.