Steven Fletcher put Wednesday ahead after 23 minutes but the Owls failed to turn their dominance into further goals and Derby extended their unbeaten home run to nine matches after Moses Odubajo fouled substitute Jack Marriott in the penalty area after 82 minutes.
Odubajo then saw red in stoppage time for a late challenge on Scott Malone as Monk's side missed out on a return to the Sky Bet Championship play-off places.
"I think that first 35 minutes we were very good," Monk said. "We quietened the crowd, we had them where we wanted them and just lacked that second goal.
"The end of that half and then the second half it became very scrappy and there was a lack of composure from both sets of players.
"The penalty and the red card changed what should have been the three points to making sure we secured the one point, so credit to the players for doing that and seeing it out.
"Overall it's another point and we'll try and keep the points coming in as much as possible."
On the incident that led to the penalty, Monk added: "Mo's in front of their player and it could be a foul on Mo and it could be a foul on him – it's one of those 50-50 ones and it's gone against us and we have to accept that."
The visitors' early dominance was rewarded midway through the first half when Fletcher put Craig Forsyth under pressure and the Derby defender's misplaced pass fell to Bannan. He played in Fletcher, whose first-time effort nestled in the bottom corner.
Derby should have been level moments after the interval but Martin headed Duane Holmes' cross over from eight yards.
The Owls had a chance to extend their advantage after 55 minutes but Fletcher headed off target from Adam Reach's right-wing cross.
Wednesday were made to pay for their spurned chances late on as substitute Marriott was fouled in the box by Odubajo and Martin converted from 12 yards.
Derby took 79 minutes to register a shot on target and on this evidence the introduction of England's leading scorer Wayne Rooney to the playing squad in January cannot come soon enough.
Derby boss Phillip Cocu said: "The key message (at half-time) was you have to find a way into the game.
"Sheffield Wednesday's tactical choice today was to play direct with no build-up and they didn't want us to play football.
"It took us maybe 30 minutes to find a good way to get good positions with the ball.
"We played more direct the second half, the team really stepped up and I'm really pleased with the second half. You have to find a way to get a result."