Fremantle so very nearly had the game taken from under its noses when Matt White goaled to put the Tigers in front with less than three minutes remaining.
But the Dockers scraped home with a late Hayden Ballantyne major for their third win of the year.
"Very relieved with the win," Johnson said.
"It was a really tough, narrow win. The boys are feeling it today.
"But we come away with four points, which is good. Very gutsy win by the team and hopefully we can carry it through for the rest of the season."
Fremantle spent much of last week analysing its poor start against Hawthorn only to concede three goals to Richmond before scoring on Friday night.
Johnson said it was an issue the club was concerned about.
"Yeah, it has been a problem the last couple of weeks," the key defender said.
"I remember them kicking the first few goals and I thought it was going to be a long day.
"I think their spread and their ball movement in the first quarter really caught us out.
"But credit to the boys, we kept on chipping away and got back into the game so that was really good."
Johnson said he had not seen the controversial non-review incident surrounding White's first shot at goal deep in the last quarter.
The 154-game veteran said he also was not aware that if the ball bounced off the goal umpire and stayed in play, without crossing the goal line, it was play on.
"No, personally I don't know. I don't know about the other boys in the team," he said.
"Whatever happened at that moment we just kept on kicking on.
"The AFL will have to review it and we'll see what they have to say."
Johnson had not spoken to teammate Kepler Bradley after the forward suffered a suspected rupture of his right anterior cruciate ligament, but he feared the worst.
"At half-time I went into the rooms and he was getting treated by the physios and he was pretty disappointed," he said.
"I think today he'll get his scans and his picture done. We'll wait and see what the results are.
"We know that Kepler is a very important player for our team and for our club and he'll be doing whatever needs to be done and hopefully he's back on track soon.
"I know the club will be there to support him and the players will be there as well."
