Having headed his side into the lead, Nottingham Forest loanee Ishmael Miller blazed his penalty over Paddy Kenny's crossbar just before the break.
Then Marek Stech's kick out of his hands hit the wind and found its way to the feet of in-form Ross McCormack for the equaliser.
Stephen Warnock's free-kick then flew over the Czech's head to seal another home defeat for the Glovers.
Johnson insists his side cannot get too bogged down by their winless run with the visit of fellow strugglers Millwall just three days away.
"We've got to move onto the next game and not try to drag them down too far and hang on in there," he said.
"The first half was really in our favour and we really should have gone in 2-0 up.
"In the second half it was in their favour and unfortunately we made the mistakes they didn't into the wind.
"Marek has been a great goalkeeper over the weeks and years but for him I'd put them down as two mistakes. We had only just said in the dressing room not to let that missed penalty affect us.
"Millwall is massive, it is one of those cup finals."