Dundee United had asked for the Clydesdale Bank Premier League match to be postponed after O’Donnell collapsed to his death during their game at Motherwell on Saturday.
The Scottish Premier League insisted the game went ahead with a pre-match tribute of a minute’s applause.
However, the sombre mood was interrupted by a series of controversial moments as Hearts ended up with eight men in a 4-1 defeat – their sixth loss in succession.
Dundee United captain Barry Robson grabbed a hat-trick at Tannadice to sink Hearts.
And afterwards Frail admitted the discipline problem is a pressing concern.
Frail said: “Indiscipline has been inherently wrong for a long time at the club.
“Having no real leadership or a specific person in charge, it has been allowed to slip, and it is something that will need to be stopped as of tonight.’’
However Frail rejected claims that his players had lacked dignity in the circumstances.
He said: “Dundee United asked for the game to be postponed yesterday and we were quite happy to go along with that but we need to take our rule from the SPL.
“The game was going ahead and they were going out there to win a game of football, although ultimately we didn’t.”
United boss Craig Levein did not change his opinion that the game should never have gone ahead and was in no mood to celebrate.
“The players were very subdued before the match,” he said. “I thought the whole card should have been cancelled on Saturday.
“The players said yesterday they would rather not play.”
Elsewhere Falkirk manager John Hughes blasted referee Iain Brines for being too lenient on Frazer Wright after the Kilmarnock defender and his keeper Tim Krul were sent off near the end of the Bairns’ 1-0 win at Rugby Park.
A Carl Finnigan header after 11 minutes put the visitors in to the lead and thereafter there were few talking points until injury-time when the Dutchman made a save from Jamie Hamill on his goalline as Kilmarnock pressed for the equaliser.
A melee involving half the players on the park ensued after Wright, not for the first time in the game, challenged the Bairns goalkeeper – who then reacted. Brines showed both players a red card and to add to the confusion, Krul was stretchered off with an injury.
But Hughes said: “If he (referee) handles it the first time then there is no problem.’’
Before the game started there was a minute’s applause for O’Donnell.
Hughes admitted to feeling uncomfortable about being so involved in a game of football.
He said: “The game should never have been played, as far as I’m concerned. We are all jumping about like lunatics for three points but when you think about it in the cold light of day you say, ’it shouldn’t be like that’.
“I think the whole card should have been scrapped but that’s for the guys at the top to decide, we only go by instruction.’’
Meanwhile Aberdeen manager Jimmy Calderwood hailed the tenacity of his players in taking a “massive three points” from their Pittodrie clash with Inverness.
Barry Nicholson struck from the penalty spot in the 83rd minute, after Ross Tokely had fouled Lee Miller.
The 1-0 victory allowed Aberdeen to remain level on points with Dundee United, who stayed fourth in the Clydesdale Bank Premier League thanks to their comprehensive victory over Hearts.
Despite his team failing to produce an eye-catching performance in the swirling wind, Calderwood was delighted to win.
He said: “I thought we started the game quite well, getting in behind them, but that petered out and then it became a battle.
“It was very difficult and the game had nil-nil written all over it.
“But we got the break and it is a massive three points for us.’’