IT was stretching things a bit for Dundee United supporters to call this a "Beautiful Day" – as they did at full time – but they were fully entitled to enjoy their spoils from this drab match on rainy Tayside.

The song has become synonymous with their vivid 2010 Active Nation Scottish Cup final win and, compared to that, the consequences of Scott Robertson's winning goal here were small beer. They sung it all the same, in appreciation of securing fourth place this season and a place in the Europa League third qualifying round.

"I think that's three years in a row we've had European football," said manager Peter Houston. "The players can be proud of themselves, especially since they only amassed 10 points in the first quarter of the season. I'm exceptionally proud of them."

Robertson's finish was good and so was United's timing: when better to play the league champions than when they are past the finishing line and freewheeling towards the summer? Celtic were the better side and created more chances, but there was an unmistakable reduction in tempo and urgency among Neil Lennon's players and the manager tore a strip off them about it after the game.

Despite a late flurry of pressure, which United withstood very well, Celtic fell to only their second defeat in the league since October.

"I'm not happy with the attitude of some of the players, some of them were in holiday mode already," said Lennon. "We were wasteful. We were a little bit slack, taking too many touches, we weren't moving the ball quickly enough, poor crossing, lashing at shots -

"We need to knuckle down again this week. We have plans for testing this week to compare their fitness now with what it is when they come back for pre-season. They were facing a tough week but it may even be tougher now. I'm not happy with them today. They'd better be ready for one final push or else they won't be going on holiday just yet."

United's 21st-minute goal came as such a surprise that many of the Celtic supporters weren't even paying attention. They were indulging themselves with a huddle, bouncing with their backs turned to the pitch until they turned to see the ball nestling in Fraser Forster's net.

United won a corner and Gary Mackay-Steven played it short to Paul Dixon, who sent over one of his characteristically fine deliveries on to the head of Robertson, who buried his finish. The midfielder is likely to leave in the summer, having so far resisted a United contract offer.

"That's probably my last goal at Tannadice, so it was a good way to sign off if that's the case," he said.

United have been far more impressive at times over the season. They worked hard and held a shape – 4-5-1 – which made life difficult for Celtic, but they were mostly defensive and pinned back.

Gavin Gunning had been out because of injury when they fell apart to lose 5-0 at Ibrox in midweek and his return to the centre of defence, at the expense of Garry Kenneth, brought solidity.

His interception prevented Gary Hooper's cross reaching Scott Brown after a clever through ball by Kris Commons, who has been Celtic's best player since the title was wrapped up. He was again bright and lively.

Celtic again went with a back three, this time Mikael Lustig, Thomas Rogne and Charlie Mulgrew. Glenn Loovens had been due to start until tweaking a hamstring during the warm-up. It was a day of knocks and niggles for Lennon. Rogne and Brown came off with hamstring and groin problems respectively. Hooper, Lustig and Adam Matthews, whose run took him careering into a trackside photographer, all took sore ones during a dull first half.

Ironically, the first man to be withdrawn, Anthony Stokes, wasn't injured although his lame performance was painful for Lennon to watch. Stokes' final touch was an awful miss in front of goal after Commons had done well to dig out a cross for him, so the manager hooked him and sent on Tony Watt.

Celtic huffed and puffed. Dusan Pernis had to save from Hooper and later Watt, but he was always comfortable. Even at the end, with Gunning off injured, United dealt with a bombardment of crosses.

Celtic shouted for a penalty when Izaguirre's cross struck Keith Watson on the hand but referee Iain Brines saw nothing intentional in it. Lennon compared it to the penalty given to Hearts when the ball brushed against Victor Wanyama in the William Hill Scottish Cup semi-final.

"I've got a three-game ban hanging over me already, but what is the difference between the penalty given against us in the semi-final and that decision today?" he asked. "You'd have to ask the referee that. I'll get accused of being a sore loser or blaming referees and that's not the point. I just want an answer. I'll maybe ring John Fleming [the Scottish Football Association's head of referee development] tomorrow and ask him what's the difference between the one given against us and the one today? You've got to be consistent."