Barry Robson's penalty in the 22nd minute opened the floodgates for the Dons in the opening 45 minutes, with the midfielder later scoring a header before efforts by Peter Pawlett and Niall McGinn made it 4-0 to the visitors at the interval.
But Caley Thistle came storming back after the interval with Billy McKay scoring twice in the opening 11 minutes before Graeme Shinnie set up a grandstand finish as he reduced the deficit to one in the 89th minute.
However, it was not to be as Aberdeen held on to move up to third in the Scottish Premiership table.
Hughes said: "We gave ourselves too much to do, which is unlike us as we've got a great record recently of clean sheets.
"However, we made a better fist of it in the second half. Indeed, I felt like we might have deserved something out of the game.
"We scored three goals, while their goalkeeper has saved from Nick Ross and we've also hit the woodwork.
"I felt Aberdeen scored against the run of play in the first half, but after the penalty they were the better team and I'm a little bit disappointed by the manner in which we conceded the next three goals
"At half-time we told the boys to go out and win the second half while giving the fans something to shout about, which we did."