Sunderland survived some significant second-half pressure to secure the points, after Carl Winchester opened the scoring from a well-worked move.
"It's definitely fair to say it was a really tough game and we knew that before," Johnson said.
"I suppose with my Sunderland rose-tinted glasses on I would say that we should have killed them off earlier in the game, we had three or four really good opportunities.
"A couple of them came from some very good, flowing football.
"They had some good chances as well, for sure, and I'm sure XG would tell you it could have been 4-3 or something like that.
"I think the fans willed us on in the latter stages.
"We were making some emotive decisions I thought, which led us to giving the ball away more often than I'd have liked but at the same time, I can't knock the too much because I've asked them to play.
"You can't have both, the intention to keep the ball but tell someone to shell it when it sits on the edge of the box.
"That's a big three points for us, because they will take a lot of points and be up there at the end of the season. By Christmas you will see them rooted in the top six, I'm fairly sure of that.
“I think we made some poor decisions on the ball late on," he added.
“When you’re out there and you’ve been a player and you want the win so much, sometimes it’s the hardest thing in the world to do to have the fire in the belly and the ice in the head.
“We had the fire in the belly today and not quite enough of the ice in the head.
“In saying that, we’ve had three or four breakaways that really we should have been more potent with. Like I say I’m pleased.
“The lads have come in and not feeling almost like they’ve won because of how much effort they’ve had to put in and I was really conscious to say that is a really good result and you’ve got to enjoy it, particularly for the next 24 hours."
Johnson hailed his full-backs for stepping up for the goal, and believes his side have more attacking potential to unlock.
"I thought our positioning in possession was poor after a good start, and it led to lads almost thinking they were having good individual performances but without doing enough for the team," he said.
"We weren't using the trigger pass or turn as a catalyst for our pressing, and there wasn't enough penetration in behind.
"We shouted on just before the goal to get our full backs higher and to be more aggressive, and it worked because we were able to go full back to full back.
"Then it's about killing teams off. I know that might sound a bit disrespectful to Bolton because they had some very good chances in between, but we had opportunities and it's something I believe we can really improve on.
"Someone is going to get beat four or five, law of averages says it with the openings we're creating."