This result emphatically ended a run of three games without a win that saw Hughes' men last week overtaken by Dundee United.
Until Saturday, the Hibs boss had been reluctant to set his side a specific target this season but he left no doubt after watching arguably their best attacking performance since he took charge last summer.
He said: "I'll go public and I'll say this: I want third spot and Europe.
"There's no point in shying away from it.
"I want it and I said that to the players.
"Let's make sure that we're doing everything to try to achieve that.
"I'm wanting it and that's the demands I'm putting on them.
"Three points today and that performance, that'll go a long way to getting us there.
"If we don't, it won't be for the want of trying."
However, Hughes all but ruled out pushing Celtic for second spot, despite closing to within two points of Tony Mowbray's men, who play tomorrow.
"You'd always like to go and challenge them," he said.
"But I think the Old Firm are miles in front of us."
Striker Derek Riordan, who scored twice, was ready to live up to the standards his manager is demanding.
"That's our main aim," he said of third place.
"We've had a good start to the season until now, so we've just got to keep pushing forward."
Anthony Stokes also scored a brace, while Colin Nish netted the 16th-minute opener, justifying Hughes' decision to restore his three-pronged attack.
But Hamilton, who have played Rangers in league and cup three times this month, created plenty of chances of their own and could have been ahead early on.
Hughes said: "For the first 10 minutes, I felt Hamilton were the better side.
"Graeme Smith made one or two saves to keep us in the game.
"Once we got the first goal, I felt for an hour after that we played some really good stuff.
"I think we caught Hamilton at the right time.
"They've come off three momentous games with Rangers."
Hughes refused to confirm or deny an interest in Preston defender Michael Hart or Celtic goalkeeper Mark Brown, joking: "I would take wee Scotty Brown from Celtic."
Opposite number Billy Reid was stunned his side were beaten so heavily, saying: "It was a strange game.
"I think we were losing 5-0 with 30 minutes to go, which I couldn't quite believe.
"I thought we'd scored early on from a set piece - the ball just didn't go in the net."
And the Accies boss hit out at the decision to allow Hibs' second goal after Stokes appeared to barge Alex Neil off the ball.
"I thought it was a clear foul - it was an easy decision for the referee to make," said Reid, whose side's consolation was scored by Flavio Paixao.
"We lost it for a wee bit.
"We've come in 3-0 (down) and I said to the players, 'We don't give in at this club'.
"The game's 5-1 but I don't think anyone could complain if their goalkeeper's man of the match."
Yet Reid admitted he blundered by playing midfielder Neil in defence, adding: "It probably didn't work and I take a wee bit of responsibility for that."