Ian Cathro’s side fell to a 2-1 loss to the League 2 part-timers and now need to beat Dunfermline on Saturday in their final Group B match to be assured of progress to the second round.
Despite victories over Elgin City and East Fife, the surprising result has once again raised questions over Cathro’s suitability for the role following a frustrating ending to last season in which Hearts won only four from 17 league matches.
Northern Ireland internationalist Lafferty, who arrived during the summer from Norwich City, took to social media to express his disappointment at the defeat.
The former Rangers forward, whose fourth goal in three games was sandwiched between a Jason Brown opener and Rory McAllister’s late penalty, said: “Disappointing result. Cup or not that performance isn’t good enough from this team. Wake up call and we go again Saturday.”
Responding to a fan who said the result would not put him off buying a ticket for the Premiership opener at reigning champions Celtic next Saturday, Lafferty said: “Nothing should put you off that ticket mate. Will be fireworks.”
Lafferty’s fellow countryman Michael Smith, who joined the club from Peterborough United, also took to Twitter in the wake of the defeat.
The right-back said: “Tough one to take but we learn from it and go again on Saturday.”