Poor defending from two Jamie McAllister free-kicks allowed Dominic Blizzard to open the scoring after 15 minutes and Byron Webster to double the Glovers' lead seven minutes before the break.
Pompey bounced back with a spirited display in the second half and Paul Benson netted after 54 minutes to give the hosts hope but they were unable to rescue a point.
Johnson said: "We knew they kept advertising the fact they've lost games on set plays. They had done a bit of scouting for us and it meant we could get in there and be dangerous. That's what we did."
Johnson admits the Somerset side is punching above its weight in League One, so he was delighted the ambitious Glovers secured a creditable win over the 2008 FA Cup winners.
"Let's be honest, we're doing all we can to fight above our weight," added the Londoner. "I give the players some stick and I do it to make sure they keep their standards and ambitions high.
"We don't want them to be shrinking violets when they come up against Portsmouth. We needed to let them know we were here for a proper game and we out-footballed them in the first half."