Arrows had taken the lead after 40 minutes at Princess Magogo Stadium through Musa Bilankulu but were let off the hook with six minutes of the game remaining as referee Lwandile Mfiki failed to spot left-back Nkosinathi Mthiyane handle the ball in the area, despite being well positioned to do so.
And speaking to reporters after the game, Johnson said: "Hard luck. I don't think it's a word hey... hard luck. Sometimes it's life and death when you’re playing games every 48 hours and then you've got 60 or 70 percent ball possession.
"And then you've got one decision not going your way which changed the game completely because I thought the goal they scored was a soft goal; we worked on it, we knew how we had to defend it, it was one set-piece I think they had.”
A silver lining to their cup exit sees Stars now able to put their full focus into their Absa Premiership campaign, where they find themselves just four points clear of the relegation zone with seven games remaining. Their next two outings are at home against fellow strugglers Free State Stars and then away to Ajax Cape Town before the end of April.
Johnson continued: ”But we'll soldier on. We are out of the cup. We give glory to Golden Arrows and we wish them well but now we can have a little bit of rest and we can prepare which is more important for us as well, prepare for the coming league games. We need those points and we need them badly.
"Never be satisfied with where you are in the league position because of the marathon runner," he added.
"Because you know everybody behind you is pushing as well and you've got to push as well.
"We are not satisfied and we'll definitely fight for whatever points are available and make sure we try and get the best results we can."
Stars will be boosted on Wednesday when they host Free State Stars by the return of captain Vuyo Mere and Sphamandla Mlilo from suspension after they missed the clash against Arrows.