'If only' is an over-used phrase among football supporters, but during the past month Norwich City fans could be excused for having uttered those words time and again.

They will have left the past four Premier League games thinking of what might have been – if only that penalty had been tucked away against Southampton, if only that penalty had been given at Sunderland, if only the Canaries had been more ambitious at Wigan, or had held on for another 10 minutes.

The feeling will not have been dissipated by events at Carrow Road on Saturday, where a tantalising first double of the season appeared to be within City's grasp with half an hour remaining as they led traditional whipping boys Swansea 2-1.

Instead, one glaring miss and one smartly-taken equaliser later, they had to settle for their 14th draw of the campaign – more than any other Premier League side – and most of those in a near full house headed home to reflect on another missed opportunity for their team to haul themselves further away from the danger zone. A mixed bag of results yesterday – defeat for Sunderland, a draw for Wigan and victory for Newcastle – left Chris Hughton's men in 14th place, four points clear of the bottom three with six games to go, a better position than appeared likely during a worrying opening half against the Swans, but less comfortable than they would have liked after getting their noses in front in the second period. It means they head to the Emirates Stadium next Saturday to face an Arsenal side in their best form of the season, and able to recall their two most notable England internationals if they feel the need. City fans who have witnessed just one victory in 15 league games will travel more in hope than expectation, still viewing the remaining three home matches as their best route to safety. A draw against the Capital One Cup winners was a fair reward for the Canaries' contribution to Saturday's incident-laden contest, but there are times when you need to cling on to three points even if it's a little hard on the opposition, and this was one of them. It was something of a surprise that Hughton made just one change after the Wigan defeat, but goalkeeper Mark Bunn's return from a one-match ban lasted just 15 minutes before he suffered a groin injury kicking two tricky backpasses upfield, giving Lee Camp his third outing in a row.

Swansea keeper Michel Vorm pushed Michael Turner's shot round the post – the provider, Robert Snodgrass, might have had a penalty for a shove by Wayne Routledge – but it was the visitors who were celebrating on 35 minutes when Spanish star Michu scored his 21st goal of the season.

He had already had one splendid goal disallowed for a foul by Luke Moore on Jonny Howson, but this time he rifled a shot past Camp after Nathan Dyer, Chico Flores and Jonathan de Guzman combined neatly.

Dyer nearly made it 2-0 before City levelled five minutes later, Snodgrass stooping to head home after Kei Kamara's deft footwork and Elliott Bennett's perfect cross.

Five minutes after the break, Camp made a point-blank save from Moore, while Russell Martin tested Vorm with a volley after Bennett had nodded the ball into his path. Bennett turned provider again on the hour, when his free-kick on the right eluded everyone except Turner, who arrived at the far post to score with a sweet half-volley.

The atmosphere was transformed and after Michu planted a weak header straight at Camp from a cross by Ki Sung-yueng, loan striker Kamara might almost have wrapped the game up, but he froze as Snodgrass crossed into the six-yard box, allowing Dwight Tiendalli to make a vital interception.Camp kept the Canaries in front when he tipped over a header from Moore from a cross by substitute Pablo Hernandez, but the reprieve was short-lived. With 15 minutes to go, Tiendalli crossed from the left, Angel Rangel headed back across goal and Moore hooked the ball in from close range. Martin sent a left-foot shot fizzing wide before Grant Holt was introduced with 10 minutes remaining, the under-employed club captain taking out his frustration on Chico with a dangerous tackle that went unpunished and a push in the face on the same player that earned him one of the eight yellow cards shown by referee Michael Oliver.

In four minutes of stoppage time, Michu could have secured victory for Swansea but blazed over, leaving the hosts with a point. It could have been better, but it might have been a whole lot worse.