The Black Cats fell behind after five minutes when Rhys Oates capitalised on a poor pass from Lee Burge, and Johnson's side again laboured in search of a response.
Though Dan Neil hit the crossbar at the start of stoppage time the visitors were good value for their win, creating the better chances in the first half and defending resolutely in the second.
Johnson, who made four changes at the break, says his side have seen their confidence drain in recent games.
He urged his players to show more and says maintaining that confidence is his biggest challenge as manager.
The head coach added that the first half was a 'wasted opportunity' for a number of players.
"I though their team worked harder than we did in the first 45 minutes," Johnson said.
"I thought we wasted 45 minutes of opportunity.
"I'm learning all the time about this football club, it's a fascinating place, and obviously I'm learning about a new squad all the time.
"I've just been talking about media, social media, and how that can have an impact. It's a really big part of society now and you've got be able to manage it.
"I think as a manager, 15, 20 years ago I think it was easier to raise confidence levels.
"It's clear right now that we are lacking confidence.
"If you rewind seven, eight games ago, we were playing compact and popping the ball around, the players were flowing over the ground.
"The first half, I thought that was a poor attitude and we were low on confidence," he added.
"Second half I was OK with, don't get me wrong it wasn't great but there was nobody hiding.
"What you can't do at a club like this is hide.
"You've got to be consistent with your confidence and try to create a vibe that is enthusiastic, to send the crowd home happy.
"We've lost games, Burton away for example, where we played with identity but ran out of time.
"Today we kept going [in the second half] and had a couple of chances, but the minute things just aren't falling for us and we've obviously gone close through Dan, but overall I thought they deserved it.
"They hustled, they harried and they had good chances on the counter.
"They deserved it.
"Our technical performance was so poor today. You can't have excuses about the pitch, the wind. Both teams are playing in the same conditions and some players today should really have made a big claim for the Ipswich game today. Frustrated that they haven't been in the team, and to show not just the manager but everybody else that they should be playing.
"It just fizzled out in terms of making that statement.
"I've got a really big job in terms of maintaining those confidence levels, and that's probably the most challenging thing in football for a manager today.
"The pattern of this football club seems to repeat for too long, and that's the bit I find fascinating.
"We're in that now, and we've got to turn that tide, we've got to buck the trend and get ourselves ready for the Papa John's game and then a very important game against Ipswich."
Johnson admitted his side's increasing habit of starting games slowly was under scrutiny behind the scenes, and says he was frustrated by another 'laissez-faire approach' from his team.
While Johnson said the 'bigger picture' is in focusing on League One and trying to achieve automatic promotion, he felt the side he picked was more than strong enough to win the game.
"We've lost a game today that we didn't want to lose," Johnson said.
"In the bigger picture, we weren't going to compete on all fronts in all of the cups and in the league.
"I wanted to win the game and I picked a team so, but looking at it, being in the quarter final of the Carabao Cup and being through in the Papa John's, the fact that we've lost is disappointing but our focus clearly has to be on the league.
"It's very difficult to legislate from the error we've conceded from, and that's probably happened too often in the last two or three games.
"But again, confidence sometimes comes from that.
"Our starts is something we've looked at and discussed.
"We credit them for their passing but were we laissez-faire? Did we expect to be able to stroke the ball around at will? You can't expect that against any side, let alone one with their best players back fit, who are well organised with a good manager.
"You've got to find time to leave it down the sides to stretch teams, and you've got to find times to play through and stretch teams.
"Nothing in our philosophy says we can't go direct, that we can't play down the sides and turn the opposition. We did it regularly against Cheltenham, for example.
"We have that speed, but for whatever reason at the moment our players are a bit devoid of confidence and are struggling with their technical decisions."
Sunderland face Bradford City in their final Papa John’s Trophy group game on Tuesday night, before a long break before the visit of Ipswich Town to the Stadium of Light on November 20th.