Jordan Parry, 16, and Darren Melrose, 18, made off with the items and left bottles strewn at the entrance behind them.
A third teenager, Charmaine Holmes, 17, who was handed an 18-month community payback order, was also with them.
The trio were spotted by a man who was paying his respects to a friend who was killed in the tragedy last November.
Police were alerted and the teenagers were caught on camera forcing their way into the pub.
Officers then heard them smashing charity tins off the pavement and saw piles of coins and bottles of alcohol.
Parry, Melrose and Holmes pled guilty at Glasgow Sheriff Court to breaking into the pub, while acting with another, and stealing charity tins, cash and alcohol.
Holmes also admitted breaching a curfew previously imposed by being out at the time.
Sheriff Joseph Platt said the two males would have been sentenced to nine months if it was not for their guilty plea.
He said: "The Crown stated the sum of cash involved is £171. While that is not a particularly large amount it was nonetheless money taken from donations presumably by customers of the pub to charitable causes. That in itself makes the theft more serious.
"The offence occurred less than three weeks after the public house in question was the site of a serious accident in which 10 people lost their lives.
"Accordingly, that you saw fit to commit this offence will have led, no doubt, to feelings of disgust among members of the public, and that term will go nowhere near the emotions felt by those who lost loved ones or friends in the incident."
He said Holmes will be supervised for the duration of her community payback order.
On November 29, last year, a Police Scotland helicopter crashed into the roof of the pub, leading to the deaths of 10 people.
The court heard that at around 2.20am on December 17, a man was standing near flowers at the edge of the Clydeside when he saw the three accused hanging around at the pub and was concerned. He contacted the police.
Procurator-fiscal depute Cecelia De Groote told the court: "CCTV operators were alerted and they were able to observe the accused outside the locus."
Parry, Melrose and Holmes were told they were being arrested for theft by housebreaking.
David Kinloch, on behalf of Parry, said he had only been in Glasgow for a matter of months when the offence was carried out.
He said his client has been the subject of attacks while in detention and plans to move out of Glasgow when released.
It was said on behalf of Melrose that he described his actions as "thoughtless and disgusting".
The court was also told Holmes has received a number of "threats and abusive behaviour" and that she regrets the offence.
It was also said on her behalf that although the Crown said she was first at the door of the pub and tried to get in, she denies that and CCTV footage showed she had no contact with the door.