Ange Postecoglou felt his late father would have enjoyed Celtic performance

Odsonne Edouard and Stephen Welsh were on target as Celtic dominated the first half and set up a quarter-final against Raith Rovers.

Kyogo Furuhashi struck his fifth goal in four starts after Carl Starfelt's mistake had allowed Liam Boyce to pull one back from the penalty spot, and a stoppage-time goal from Hearts substitute Aaron McEneff only disguised the margin of Celtic's domination.

Celtic had 35 shots at goal to the visitors' five with former Hoops goalkeeper Craig Gordon keeping the score down.

Postecoglou had previously admitted his father Jim's approval was his main driver as a young manager, after his playing career as a functional defender did not quite satisfy the Greek-Australian's love of free-flowing football.

"That's the kind of football my father instilled in me," Postecoglou said. "He's up there now, but I always envisage him in the stands and think about what he'd say about the team.

"He was never that enraptured by results, he just wanted to see a certain type of football. I know he would have been off his chair in the first half especially.

"We played great but more importantly, the players enjoyed it and they got their rewards.

"I thought the first hour we were really good, the best football we played this year. We dominated and the only thing we didn't take advantage of was some unbelievable opportunities to put the game to bed.

"The football was outstanding, the intent was outstanding. We never took our foot off the pedal and credit to the players, in the middle of a heavy schedule, that they were able to push that far in.

"The last half hour we got a bit ragged for sure, a bit of fatigue set in, some lapses in concentration, but I was really pleased with the football we played.

"You are never going to totally dominate a game for 90 minutes. It doesn't matter who you are, there's always going to be times when the opposition get into the game."

There was no frustration on Postecoglou's part that the score did not reflect the pattern of play.

"If your standards drop a little bit, then you can very well be punished," he added. "But that's what keeps you honest, it just keeps us motivated to keep improving."

Postecoglou has revealed Ryan Christie is a doubt for Wednesday's Europa League play-off first leg against AZ Alkmaar after missing this game with a minor injury but Liel Abada is expected to return.

Hearts boss Robbie Neilson was happier with his side's display after bringing on winger Josh Ginnelly for midfielder Andy Halliday - who had a slight knock - and changing shape.

"I thought in the first half we were too passive at times," he said. "When you come to Celtic Park you have to be on the front foot, you have to make tackles, you have to be aggressive. We didn't do that.

"We allowed them to pass it about too easily. We changed it at half-time and that allowed us to get more positivity into the team. I thought in the second half we were much better.

"We knew that Ginnelly wasn't going to be fit for the start of game. We knew we were only going to get 30 or 40 minutes out of him.

"We brought him on at half-time and his pace changed the game. It allowed us to get up the pitch."