I remember the last game Dundee won in Leith. A callow youth that had just started high school, I journeyed to Edinburgh for a rare away day with my brother, who lived in the shadow of Easter Road at the time, to see the Tayzzuri take on the Cabbage and Ribs. We ended up on the front page of a national newspaper as part of a jubilant Dundee support celebrating a last-minute winner by Stevie Milne, my eyes gleefully fixed on a sullen, catatonic home support.

There was to be no such glee this season, though, as we turned in for 90 minutes everybody in dark blue would rather forget, not least Trevor Carson, who had what can only be described as several rushes of blood to the head all at once to gift Hibs their opener. Defeat leaves us in what feels like a two-way battle for sixth spot as we enter the home stretch. Hibs are the only bottom-six side we've lost to all season, and I can only hope that doesn't prove crucial once we hit gameweek 33.

Our poor away record to teams that play in green and white is, believe it or not, matched by our efforts against Celtic, who we face in midweek. A May 2001 double from Fabian Caballero in a post-split dead rubber at Parkhead marks the last occasion we smuggled three points out of the east end of Glasgow. Celtic's apparent troubles this season should give a fair few teams in the league hope of carrying out an upset, but history is not on our side. Unfortunately, our performances in this season's big games haven't been, either.

While we have come through a few sticky patches and come up with the goods late on in matches this season, I can't shake a deep, nagging frustration at our inability to rise to the occasion. Most matches this season can be labelled as high-pressure occasions, such is the tightness of the league and the rare opportunity still very much in our hands to secure a top-six spot and push Killie and St Mirren for a tilt at European competition (well, the qualifiers, at least). Nevertheless, at the points where the fans and even the pundits think we might be on the verge of a statement win, things have gone south very quickly.

In the League Cup this season, thanks to being the televised game in the final round of fixtures, we knew at kick off that a two-goal victory over Caley would secure a last-16 spot, but only managed a 1-0 victory. In the Scottish Cup, a mild goalkeeping crisis turned into a goalkeeping calamity as we surrendered two goals in three minutes away to Killie to extend our ignominious trophyless run to 114 years. In the Premiership itself, big travelling supports have made their way to Paisley and to Leith to face teams on poor runs of form, only to head home after bearing witness to our two poorest performances of the season.

It feels a bit churlish, or reactive to the point of whiplash, to pick at these scabs when Dundee remain in the top six with a more-than-comfortable cushion to the bottom two spots. After all, as I'll repeat until I'm blue in the face, for a newly promoted team that has overhauled its entire squad to look so at home in the top tier is an achievement in itself. However, with progress and improvement comes higher expectations and goals, and the financial benefits of a top-six finish - the larger gates, the prize money, the potential for Europe and therefore being parachuted into a later round of the League Cup - could make a huge difference to the business we can do in the summer. Setting our sights too low and continuing to humbly profess that survival would be gratefully received suggests a lack of ambition that can, in turn, become a self-fulfilling prophecy. Given the level of performance that we know the team can deliver, it's fair enough for us to raise our expectations.

I still feel confident that we'll make the top six. The clown-car that is Aberdeen FC has dropped out of contention along with Motherwell and St Johnstone, leaving ourselves and Hibs to duke it out for the final berth in the top half of the table. Facing both Celtic and Rangers before the split isn't ideal for us, but our other five games are all eminently winnable. Maximum points should be the target for our home ties against Killie, Aberdeen and Motherwell, and we should be aiming to take four points from away ties against St Johnstone and Aberdeen, too. Assuming we stay true to our rotten record against the Old Firm and gain nothing from those two games, those 13 points would put us on 45 points, which would have been enough to secure top six in seven of the last 10 seasons.

It's a tall ask - after all, were Dundee consistent, we'd already be renewing our passports - but avoiding a morale-sapping shellacking in midweek and then getting the ball rolling against Killie on Saturday is within our gift. And, if all else fails, at least we won't have to play bloody Hibs again this season.