A scrappy spectacle was settled just before the break when Massimo Luongo cashed in on a mistake from former Barnsley defender Liam Lindsay to score the only goal of the game and register goals in consecutive home matches in an indentikit 1-0 victories for Wednesday.
Tuesday's result saw them move up to third place in the Championship table as the Owls cast aside the blow of a controversial late concession in Friday's 1-1 draw at Cardiff City to post another victory.
Monk said: "We got a deserved lead and possibly could have scored more. In the second half, some bits were a little bit self-inflicted with cheap free-kicks and scrappy bits and in terms of the last two games, we have had to dig in and battle and show the other side of it.
"In a sense, you are seeing everything you want to see from a team. But of course, when we look at the two second halves, we know we can do better, especially with the ball, than we have done.
"But what you have to do when it is not going for you is show that organisation, spirit and fight and we have shown that in the two games. We are very unlucky not to be sat here after two similar games with six points.
"It was a goal that never should have been allowed and we should have been sat here from six.
"But I am very pleased with the players, we are progressing and doing well and we know what we need to get better. It will take time, but in the time you get there, you have to keep accumulating points and results and we have shown that on quite a consistent basis so far."
Meanwhile, Monk confirmed that goalscorer Luongo came off with an ankle knock, which does not appear to be serious.
"He has picked up a knock, but it does not appear to be too serious. So we will assess him when we are back in tomorrow (Wednesday), he added.
"I saw him in the changing room and we had a quick chat and I said: 'Are you alright and he said yes.' It is not too bad, just more precautionary than anything."