The World Cup debutants defeated test team Bangladesh by 74 runs after scoring 243 for seven and then dismissing them for 169 in the 42nd over.
It was Ireland's second upset victory of the tournament after beating Pakistan in the group stage to oust the 1992 winners.
For beating a second test-playing nation, Ireland now join the top-tier teams in the one-day world rankings.
It was the perfect response from Johnston's side having been thrashed by defending champions Australia on Friday by nine wickets, after getting bowled out for just 91.
'BEST GAME'
"It was the best game of cricket I've been involved with in my four years with these guys, it was the best all-round performance that we've had -- all three disciplines were outstanding," Johnston said in a news conference.
"We had to bounce back from the disappointment against Australia when a lot of people were saying a lot of things about us. We had a good chat after that game and we set new goals," he added.
Australian-born Johnston was as pleased for the fans, who had travelled to Barbados having seen the team qualify unexpectedly, as he was for himself and his team mates.
"Lots of people spent a lot of money to come over and watch us play two games of cricket and in a huge game against Australia we were nothing short of disappointing so we had to turn that around quick smart and the guys did that," Johnston said.
"I'm pleased with the level of effort the guys put in because it was a first-class effort from a team that deserves to be playing this level of cricket."
With their final World Cup match approaching against a Muttiah Muralitharan-inspired Sri Lanka in Grenada in three days, the skipper said celebrations would be short-lived.
"We've got a pretty big game on Wednesday," Johnston added. "So we will have a couple of quiet ales tonight but after Wednesday we have got three or four days (spare) so, as the coach says, we can set the dogs loose then."
The victory took Ireland above Bangladesh to seventh in the Super Eights standings on a superior run rate. Both teams have two points.
The seven-week World Cup culminates in the final in Barbados on April 28.
