In three of the past four seasons, the capital side have pushed on to the final and the Gorgie gaffer said that the ambitions have not dipped below that after seeing their way past Hamilton. “We started really well, controlled the first half and got a goal but not getting a second goal puts you under pressure,” said Neilson. “In the second half we were slack and for a period we started overplaying and they put us under pressure. Bringing [Alan] Forrest on gave us that lift.”

Stephen Humphrys slotted home the 28th-minute opener and Alan Forrest’s delivery which set up Cammy Devlin for the second, decisive goal 11 minutes from the end. But while the result sees them safely into Monday evening’s draw, Neilson would have liked a more enthralling display, especially in front of the near-4000 travelling fans – a record away crowd for New Douglas Park.

“You want to put a performance on,” the manager continued. “We brought 4,000 on a cold rainy day and you want to entertain them. At times we did, at times we didn’t. You’re at Hearts, you’re expected to get to the latter stages [of the cup competitions] but now we can relax for the weekend and see the draw on Monday night.”

Hearts manager Robbie Neilson and Robert Snodgrass celebrate the win over Hamilton.

With captain and top scorer Lawrence Shankland suspended, Neilson praised the way Humphrys stepped up to lead the line, after grabbing the headlines with his long-range lob last weekend. “He’s a finisher and he gets into the box and can shift left and right foot,” said Neilson. “I thought he was bright and there’s still lots to polish up but he’s a threat. And, they all don’t need to be from 60 yards! It was good to see Cammy back, he did well to get a tackle for the goal.”

Neilson’s Hamilton counterpart John Rankin was pleased that his side were able to punch above their weight for periods in the match and give the third-best team in Scotland a run for their money.

“If we had started the game like [we did in the second half] we'd have got picked off especially after playing 120 minutes on Tuesday,” said Rankin. “So I felt we had to be organised, compact and hard to beat in the first half. I thought we did that. Hearts had large spells of the game but I felt we were passive at times, didn't lay a glove, which disappointed me.

"We said at half-time, stay in the game for 10 minutes and we'll have a right go. And we did, and I can't ask any more from my players. I learned that we need more in the final third and we procrastinated over the final touch, the final pass, the final cross. Just put the ball in the box, you're playing against good players and if you think about it too much you are going to lose the opportunity. The players learned that but overall I'm really proud of them. It's been a tough week. It was a free hit to play Hearts and for 25 minutes we put them under pressure."

Robbie Neilson laments lack of entertainment for Hearts fans and singles out his second-half gamechanger