Dean Smith was pleased Norwich showed some fight to beat their relegation rivals Burnley 2-0 but conceded Premier League survival remains a “tough challenge” for his bottom-of-the-table club. Pierre Lees-Melou’s side-footed effort after nine minutes put Norwich ahead at Carrow Road and Teemu Pukki wrapped up the points in the 86th minute with a composed finish. Burnley had their moments and Maxwel Cornet missed a great chance to level in the second half but it was Norwich who ended their long winless run. A first victory in 10 attempts was not enough to move the hosts off the bottom and they sit seven points adrift of safety, but Smith praised his side’s spirit. “It was nice and important to get the performance and the result because it shows everybody in the dressing room but more importantly to the fans that we are still fighting,” Smith said. “We have never given up on the challenge and it is a challenge. “I have to be realistic about how tough the challenge will be but I have seen challenges overcome many times. None more so than with my assistant Shakey [Craig Shakespeare] with Leicester so who knows if you win two or three on the spin, the world and table looks a different place.” Leicester’s great escape in 2015 – where they had been bottom for most of the season – has long been a point of reference for Norwich given Shakespeare’s arrival alongside Smith in November but with games running out it felt like a last-chance saloon when 18th-placed Burnley visited Norfolk. Any momentum the visitors built from a crucial midweek win against the struggling Everton soon went when Lees-Melou’s effort deflected off Josh Brownhill and into the bottom corner. After a bright start by Norwich, Burnley improved but rearguard defending was followed by Pukki’s ninth goal of the season from Mathias Normann’s wonderful defence-splitting pass. Next up for the Canaries is a trip to Old Trafford on Saturday but Smith, who secured a 1-0 victory there with Aston Villa in September, is positive. “I’ve already won there so why not go there and win again,” he said. “Listen, we know it is a tough place to go and they will be smarting from their result yesterday [to Everton] and they will look to put it right. “I did think we were really close against them here and it still annoys me the penalty that was given that won United the game. We certainly didn’t deserve a loss in that game but it will be a tough ask, we know that, but we will not shy away from it. “We have just had two clean sheets which gives us confidence and we have to take that to Old Trafford.” The Burnley manager, Sean Dyche, was frustrated his team could not build on their 3-2 triumph against Everton last Wednesday and with the Toffees able to beat Manchester United on Saturday the gap between the Clarets and safety is back to four points. “The feeling is that it was a big step forward in the week and a big step back today,” Dyche said. “After a really strong second half against Everton and win, we came down here and could not build on that. We couldn’t find clarity in the final third, which has been the story of our season.” The key moment arrived in the 65th minute when the substitute Dwight McNeil picked out Cornet at the back post, but Burnley’s leading marksman sliced wide from close range. Dyche said: “Obviously Maxwel’s chance is a golden one and they have got to go in. We had a golden chance to change the whole feel of the game and didn’t take it.”