Celtic clinched the domestic treble with a 3-1 Scottish Cup final win over Inverness Caledonian Thistle at Hampden Park. The showpiece occasion was played against the backdrop of mounting speculation around Tottenham’s interest in Hoops boss Ange Postecoglou, who again had Kyogo Furuhashi to thank for his contribution. The Japan striker struck for the 34th times this season in the 38th minute of an otherwise nondescript first half to undo the good early work of Billy Dodds’ rank outsiders. The Championship outfit, who had not played a competitive game for a month, fell further behind when Hoops’ half-time substitute Liel Abada slid in a second in the 65th minute. Caley substitute Dan MacKay pulled a goal back with five minutes remaining, only for Portuguese winger Jota to restore Celtic’s two-goal advantage as the game slipped into six minutes of added time. It is the eighth time Celtic had completed the clean sweep of League, League Cup and Scottish Cup - a world record - and now eyes turn to see what the future holds for Postecoglou, who is the fifth Parkhead manager to win the treble. Postecoglou has been heavily linked with Tottenham Hotspur and wouldn’t be drawn by questions about him possibly leaving. “I think I deserve to enjoy this moment just like everyone else. I worked really hard for this moment,” Postecoglou told the BBC. “There will be a time to come for those kinds of questions but for now, we’ve grasped a small chunk of history for ourselves and I’m not going to pass that by by being sidetracked.” Joe Hart said: “When you are around amazing footballers and top managers, the noise is always there - but that is all it is. “We are privileged to be on the inside and today was the focus all week, the manager made that very clear. “Whatever happens now will (happen) - it is the world of football, full of speculation and rumour, but the facts today were we had a treble to focus on and we did it.” Celtic defender Greg Taylor reflected on the "historic" day for the Glasgow club following another domestic treble. "The manager's motto is he wants us to improve every day, not to waste a training session, never mind a game. That is the reason why we have had this success," Taylor said. "Some players go through their career not winning one trophy, so to win three in a season is really special. "It says everything about the group of players, the staff and fans. It has been a collective effort." Celtic captain Callum McGregor paid tribute to the work of Postecoglou in turning the club's fortunes around. "You have got to bounce back when you suffer, you have to pick yourself up and get the lads to rally around each other, and that is what we did," McGregor said. "The manager came in and the group of boys that were left, we felt like we had something to prove. "It has taken us two years to get our trophies back, and the boys have worked ever so hard. We just have to enjoy the day." Read More How Ange Postecoglou restored Celtic’s dominance and became Tottenham’s first choice ‘We never stop’: How Ange Postecoglou became Tottenham’s first choice Erik ten Hag wants Manchester United to use FA Cup final defeat as motivation Man City vs Manchester United LIVE: Latest FA Cup final updates