Hearts readily confessed they had luck on their side in seeing off Falkirk in the Scottish Cup but Andy Irving is fully aware they will require more than good fortune if they are to ease their league concerns.

Three times the hosts struck the frame of the goal early in the second-half as they made it an uncomfortable Saturday night out for Hearts amidst dreadful conditions blown in by Storm Ciara at the Falkirk Stadium. The Bairns more than held their own and could also point to carving out the best opportunity of the opening period.

However, Sean Clare’s 51st-minute penalty proved the decisive moment in amongst the driving galeforce winds and the swirling rain. After shipping six goals in drawing with St Johnstone and losing to Kilmarnock, avoiding the potential banana skin ensured it was a case of job done for the Jambos.

They can now dream of cup success but, with Wednesday night’s trip to face Celtic the first of their tests, Irving accepts there are greater challenges on the horizon as they bid to lift themselves off the foot of the Premiership.

“No-one will say no to a cup run,” said the midfielder, who enjoyed a loan spell with Falkirk last season. “It’s good getting through to the next round and it’ll give us that bit of confidence for the next league games, which are massive.

“I hope them hitting the woodwork three times is a sign our luck is changing, but we need to make it turn ourselves to be honest. It’s down to us. The league is paramount. We want a cup run as well but it’s paramount we stay in the league.

“We were underdogs against Rangers and will be against Celtic. It’ll be a tough game, no doubt. They’re in good form but when you see what happened against Rangers we’ll go there with belief. It’ll be different at Celtic Park, it’s a bigger pitch and we’re not at home so it’s maybe a bit more difficult.”

The clean sheet was one positive for Hearts. Manager Daniel Stendel kept faith with on-loan Manchester United goalkeeper Joel Pereira following some questionable displays of late and a shut-out will do the youngster’s confidence no harm.

However, it was a match of fine margins for Falkirk. Declan McManus was the first to strike the woodwork, just a minute after Clare’s penalty, which was awarded because of Michael Doyle’s nudge on Liam Boyce. Swivelling on a loose ball at a corner, McManus fired his shot off the upright and moments later hit the same post with a low effort from the right side of the box.

Five minutes later, as the Bairns held sway in their hunt for an equaliser, Gary Miller pinged a drive off the crossbar and Hearts eventually recovered their poise to see out the victory.

“We knew we were playing against a very good team,” said McManus. “No matter where they are in the Premiership, they are still a team with a lot of talent and experience. I think we handled every part of their game pretty well. Obviously, I’ve hit the post twice, Gaz has cracked the bar. It’s one of those where a wee bit of luck gets us back in the game and we might even go on and win it. We had momentum then.

“I think we started the better team. The penalty is a mistake but that happens. We reacted really well and hit the woodwork three times. If one of those goes in, Hearts might have been a bit shell-shocked that we were back in it so quickly. We gave more than a good account of ourselves, individually and as a team.

“I think most people would agree that we deserved at least a replay, I’d like to hope so anyway.”