The latest point came from Saturday’s 1-1 draw with Cardiff and Bruce feels the Tigers’ points return so far represents a solid start to life back in the top division.
“When you consider that for one of our games, we played with ten men for 70 minutes, you’ve got to be remarkably happy with what we’ve done,” said Bruce.
“We’re under no illusion as to how difficult it’s going to be and every game is going to be tough, but we’re making a fist of it and we’re up and running.
“Hopefully we can still improve.”
Although happy with the number of points picked up, Bruce knows that it could have been more had his side been more clinical against Cardiff at the KC Stadium at the weekend.
A Curtis Davies opener just before half time was cancelled out by Peter Whittingham after the break, but with the Tigers creating the better chances it was another afternoon tinged with frustration.
“We produced the best chances in the game, but how many times have I said that in my 15 months here,” added Bruce.
“Cardiff had one shot on target and scored and that is where we have to improve. We can say we’ve played well again, and really well in spurts, but......and it’s that but that is aching away at us and we have to improve on that.
“With the goal that we did score, it was a great ball from Tom Huddlestone and we need more of that from the team in terms of being on the end of set-pieces. Curtis has had a wonderful start to his career here and chipped in with a goal, he can be pleased with the way he’s started.
“For their goal, we were ball watching a little bit and their man has run inside Elmohamady.
“We all know he (Elmohamady) is a wing-back, he’s playing at full-back and he hasn’t opened his body up and allowed their man to nip in front of him. When Whittingham gets a chance like that you know he’s going to take it.”
Bruce will keep an eye on Robbie Brady this week after the Irish international came off in the second half struggling with a sore groin.