Dickov, once a hero of the Manchester City faithful, earned a penalty and coolly dispatched it to keep the visitors on course for a memorable victory.
Adams said: "From where I was sat it looked a clear penalty. He is called The Pest and that's why people don't like playing against him.
"We won't get too carried away by this win. It's one win and what we've done is put ourselves back in the pack."
Manchester City boss Kevin Keegan was understandably disappointed with his side, who could have gone fourth had they won.
He said: "I don't think Ian Walker had a save to make all day. You have to put some thought, passing and work rate into it.
"We didn't look like a team going for what is effectively a Champions League place today."
The Citizens had a day when nothing went right.
Without David Seaman, who failed a fitness test on a hamstring injury prior to the game, rookie Danish keeper Kevin Ellegaard made his debut in goal for the home side. One of the first things he had to do was pick the ball out of the back of the net.
The home side had been pressing without luck in the opening stages, but they failed to close down Leicester midfielder Jordan Stewart on 12 minutes and paid the price.
Stewart picked the ball up just inside the home half, the home defenders stood off him and he took full advantage, advancing to the edge of the area and curling a shot past the outstretched hand of Ellegaard and into the Citizens net.
Leicester were more than happy to sit back and protect their lead and Keegan's outfit gave them few problems as the half progressed.
Marshalled by the impressive Muzzy Izzet, Leicester's game plan of hustling, defending in numbers, and snapping at opposition heels worked a treat, and just eight minutes after the break they went further ahead.
Dickov, returning to the club where the fans adored him, turned from hero to villain.
He went down under what looked to be a soft challenge from Sylvain Distin to earn his side a penalty, much to the disgust of the home supporters who made it clear to the player he was no longer their idol.
He stroked home the penalty with ease and when Marcus Bent rose virtually unchallenged to head home Leicester's third six minutes later it completed a brilliant win for Adams' side, who still have it all to do if they are to survive in the Premiership this season.