Perisic scored Inter's third goal to seal the victory after Adem Ljajic and Mauro Icardi had struck in the first half, although Franco Vazquez had pulled a goal back for the visitors before half-time.
Inter's third successive home league win keeps them in fifth place in Serie A and Mancini picked out Kondogbia and Perisic as the star performers at San Siro.
"Ivan Perisic is simply getting to know Italian football, which is very different to the Bundesliga," he told Mediaset Premium.
"Geoffrey Kondogbia is improving too and both will be the future of Inter."
But Ljajic was criticised by Mancini despite the Serbia international giving Inter the lead with a superb run and finish in the 11th minute.
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"I really, really like Ljajic and he knows that, but at times he doesn't train with the right attitude," Mancini said.
"His feet are excellent, but his brain doesn't always work properly.
"He can sometimes rest on his laurels during a game or train badly all week.
"A player with his quality should make the difference always, the way he did tonight. There are few players out there like him."
Mancini added that anything can happen for Inter, who are five points behind Roma in the race for Serie A's third and final Champions League qualification place - with the Nerazzurri travelling to the capital on March 19.
"I don't know if it will be a decisive match, as when there are still 10 rounds to go, anything is still possible," he said.
"We created some enormous expectations at the start of the season, albeit realising we didn't have the resources to stay up there at the top of the table.
"Our target has always been third place and we're still in the running."