Aziz Behich's early goal proved to be the difference between the sides in what was a frantic encounter from start to finish.
Despite dominating the majority of possession and creating plenty of chances, the Hibees couldn’t find the back of the net and United held on to claim their second win of the season.
Speaking to Hibs TV after the match, Johnson was frustrated with the result but could take the positives from the performance.
"It was a very disappointing night but I honestly thought we played well in the second half.
"We had seven really good chances across the game, Dundee united had a few as well. So much of our game was good, but we have been let down by some poor defending and a combination of poor finishing and great goalkeeping."
The Hibees carved out several goalscoring opportunities throughout the course of the 90 minutes and had a goal controversially ruled out in the first half. Mykola Kuharevich turned home following Elie Youan's acrobatic effort, only for the referee to call the play back for a foul in the build-up - a decision which Johnson disagreed with.
"The goal we scored, how he has given a foul there I will never know. It was given for a foul in the build-up for a push, not for the high foot so that was a bit of a shock to us and to me and I don’t think we deserved that.
“But it was one of those days where our finishing wasn’t good enough and the ball just didn’t fall for us. However, there was a lot of good stuff in there as well."

Boyle, Kuharevich, Porteous and McKirdy all had chances to draw the game level but ultimately we weren't clinical enough in front of goal and couldn't find an equaliser.
"You have to put the ball in the net," said Johnson.
"The game is about putting the ball in the net. You can play a horrendous game but you can have one fantastic finish that makes the difference.
“I think we played in the right areas a lot of the time, McKirdy was good when he came on and caused them problems with his movement and his energy. I really like Mykola, he will be a top player for us, but when he is 1v1 with the keeper he has to score.
“The fans stayed behind to clap the boys off for the effort that the lads put in. They saw that if we played that game 100 times, we win it more times than not."
Watch Lee Johnson's post-match reaction here!