"Connacht have beaten both other Scots sides already this season and they are a very committed side who play for the full 80 minutes," he said.
"They have a couple of good goal kickers in their team. You have to be on your guard so that you do not present them with opportunities to get the scoreboard ticking over. And you certainly cannot afford to take Connacht lightly – I think everyone in the Celtic tournaments are well aware of the threat they can pose.
"The Celtic Cup represents the one-off occasions, when you can go for it, as we did against Celtic Warriors last Friday. But a home game in the week-in-week-out demands of the Celtic League is where you have to have the consistency so this is a big game for us, a very important match.
"We have to perform, no question about that, if we are going to do anything in the League this season. We have got a few injury problems, like at scrum half and in the centre, but I feel we have the cover in the squad to cope with those concerns."
Glasgow produced the upset of Round 1 in the Celtic Cup competition when they beat Celtic Warriors 19-9 at the Brewery Field last weekend but Hugh is only looking at the next challenge.
"We played pretty well – and Celtic Warriors missed a few chances they would normally expect to have taken," he said. "But to get a win away from home was achieved with a great attitude from the players and now we must carry that forward to the clash with Connacht."