A clever strike by Shaun Maloney and a controversial goal from Gary Caldwell gave the champions a comfortable win against a 10-man Jambos side who had defender Marius Zaliukas red-carded for a 'last-man' foul on Scott McDonald, although Paul Hartley sent the resultant spot-kick wide of the target.

It is thought that someone from corporate hospitality at Tynecastle verbally abused the Hoops boss as he came out from his post-match media briefing.

A Hearts spokesman said: "An investigation has already started and once the individual has been identified, appropriate action will be taken."

Strachan, who claimed he knew nothing about a newspaper story that Barcelona defender Sylvinho was a target for the Scottish champions, praised his side for their commanding win.

However, ahead of the visit of Manchester United in the Champions League on Wednesday, Strachan was at pains to highlight the abilities of the tournament holders who beat the Hoops 3-0 at Old Trafford in the first game.

The Celtic boss said: "It was a hard game until the two goals went in and it was good that the players put themselves in that position. After that we could come down a couple of gears.

"People have spouted that Manchester United played in second gear against us.

"They were only in second gear when they got to the stage where they had scored two goals against us and remember, those two goals were offside.

"Everyone in the United camp said that it wasn't easy for them, it was hard work.

"They couldn't find a way through and Artur Boruc didn't have a shot at him.

"Whatever happens, we won't have the same ability as them, you know that and I know that.

"They are the best team in the world, they are far better than Italy and France.

"That's the competition we are playing in.

"West Brom were there previous to us and lost 4-0, Hull have lost four, West Ham have lost two and it could have been any score and Roma lost seven.

"Whatever our failings, spirit, character and determination is not a problem

"But we will need to be at our best and have a bit of luck against them."

Hearts boss Csaba Laszlo insists his side struggled after going behind so early once again.

He said: "The loss of the early goal was key.

"Every game we are going a goal behind and it is terrible.

"We went a goal behind to Hibs and then Aberdeen and then Celtic and we have to concentrate more.

"We were two down in 20 minutes and the second goal was like a knife in to us.

"When I saw it again, it showed that there was a hand used but I am not criticising the referee, it was hard for him to see it.

"I am always disappointed when we lose a game but I wish Celtic good luck for the game against Manchester United."