DUNDEE have lost their place in the Scottish Premier League but cling to their resolve.

Defeat by Kilmarnock was conducted in a way which suggested they have not let relegation get them down; determination perhaps not too surprising for a side marshalled by John Brown. The Dundee manager was able to prolong the scrap to avoid the drop and took his pitch-side place at Dens Park, having decided to fight a one-match touchline ban.

That refusal to accept the will of others was evident again yesterday, with Ryan Conroy and substitute Mark Stewart's goals ensuring Kilmarnock were never able to get comfortable. "At 3-1 down they could have just chucked in the towel – but they kept going," said Ray Farningham, the Dundee assistant manager left to speak in Brown's stead.

Yet Dundee – whose veteran goalkeeper Rab Douglas said his goodbyes at half-time after his release this week – have been unable to compete against the key figures of their season; 30 points, 11 home defeats, 28 goals, and Peter Pawlett. The Aberdeen midfielder's dive last week punctuated the draw which ultimately put Dundee down, so it was hardly a surprise that a few tumbles from Kilmarnock winger Chris Johnston drew derision.

"He doesn't dive and I was angry with the crowd," said Kilmarnock manager Kenny Shiels. "He was fouled. Scottish people need players like him, guys who go on a pitch and entertain. He is no angel, but is a good footballer."

The 18-year-old was one of six players promoted from the periphery to the starting XI. Young faces are prone to blemishes, though, and the complexion of Kilmarnock's performance became pockmarked after 19 minutes; Gary Irvine's low pass across goal prodded home by Conroy. Rory McKenzie and Johnston gave Kilmarnock leads, but they always seemed at risk, Conroy only denied a shot at a second when Kilmarnock goalkeeper Cammy Bell pinched the ball off his toes.

The sense of vulnerability had been accommodated by some unconvincing defending. Irvine skipped past Ross Davidson to cross into the penalty area after 10 minutes, Lewis Toshney burrowed into the box before shooting tamely wide a minute later, while Mohamadou Sissoko – Kilmarnock's most experienced defender, but who hid that identity well – later failed to cut out a pass, allowing John Baird to worry Bell with a shot.

Sissoko had already been replaced by the time Dundee scored their second, the ball lifted over Bell by Stewart after Irvine's long pass.

Kilmarnock continued to find respite in the form of Johnston, though. The winger still looks like his mum might have dropped him off outside the ground, but he has matured into a threatening presence for the Ayrshire side, seizing on the rebound of his blocked shot to steer past Steve Simonsen for the visitors' second.

McKenzie had whetted the appetite when he ran from inside his own half to open the scoring after just five minutes and Sammy Clingan adopted a direct approach for Kilmarnock's third after 73 minutes – thumping a volley into the net following a cross from substitute Rabiu Ibrahim. "The first goal was very special," added Shiels.