The young Hoops beat Dundee United 2-0 at Tannadice to pip Old Firm rivals Rangers to the prize, with Jamie Lindsay and Paul McMullan the goal heroes.
Celtic went into the game on the back of a 2-0 derby win against Rangers on Tuesday, and knowing that only a win would be enough to keep the title at Paradise.
Frail said: "It has been a tough season with a lot of hard games, so to go and get a fifth title makes it probably the sweetest one.
"We've got a team out on the pitch to try and win the cup and the league, but our job is to product individual players for the first team.
"So we have to make sure that, as well as winning the league, we're promoting and developing these players as best we can."
Kennedy added: "Yesterday we just told the players to trust themselves and have belief. There was probably more pressure on them than against Rangers.
"It's been a big challenge, but the players have delivered again. It was important to get the second goal. If we'd gone in at only 1-0 it would have been very nervy.
"The second goal gave us a bit of a cushion and took some pressure off and we were able to see it out."