Play was allowed to continue in the 60th minute following Song's rash-looking tackle on Mame Biram Diouf, and the Hammers were able to move the ball upfield with Stewart Downing, from whose cross Enner Valencia headed in to make it 2-1.
Hughes said after the Barclays Premier League contest: "It was a poor challenge by Song - he dived in two-footed, with both feet off the ground.
"Thankfully Diouf jumped out of the way, but the referee should have stopped the game there and then
It was a dangerous challenge.
"He might argue he tried to play advantage - well, we didn't gain one
We were at a disadvantage because they go up the other end and score their opening goal.
"It is a poor decision from the referee and he needs to do better than that."
Asked whether he thought play would have been stopped if it had been a Stoke player making the challenge, Hughes said: "I can't say that
But I can think it, maybe."
And then asked if he felt Song should have been red carded, Hughes added: "He didn't catch him, but there was the potential because he was out of control.
"Referees are told - for want of a better phrase - to stamp out those challenges, but he didn't do anything about it
I don't think he even talked to him after.
"He is one of senior referees and he has to better than that."
West Ham boss Sam Allardyce stressed Song's tackle had happened some way back from where the goal was scored.
"I could see a lot of challenges that should have gone our way that went theirs, and vice-versa," Allardyce said.
"We had an awful long way to go to score, because that challenge, if I remember correctly, was only about 10 yards outside our box
It wasn't as if it happened on the edge of theirs and we took it and shot into the net.
"We played brilliantly from that ball retention, down the right hand side with a brilliant cross from Stewart Downing and a fantastic header from Enner Valencia."
West Ham subsequently equalised in the 73rd minute through the same combination, Valencia crossing and Downing firing in.
Allardyce, whose side had won four of their previous five games and are fifth in the table, felt the Hammers showed great character to salvage a point, and had particular praise for Downing.
"It was a point that was well-earned and maybe not deserved, but that's the way the Premier League is," Allardyce said.
"We haven't played as well as we want to, but we have got something out of the game, which speaks major volumes for the character of this team.
"Downing was outstanding
He has flourished in the hole again.
"We started with him out wide, but once we brought him back into the middle again he started getting into the areas much better and was much more dangerous."
Stoke had deservedly led 2-0 thanks to goals from Victor Moses - his first for the club - in the 33rd minute and Diouf in the 56th.
Hughes was pleased with the performance in many ways, but ultimately rued his side's missed chances as he was denied the perfect 51st birthday present.
Asked if it counted as happy birthday, Hughes said: "Not particularly
I'm getting old and we didn't win, so it's not a good combination.
"I thought we were excellent - it was arguably one of our most creative and dynamic performances this season.
"But we need to convert more chances than we did, because we were by far the superior team."
Regarding Moses - recently at the centre of controversy when he was branded a diving ''cheat'' by Swansea boss Garry Monk - Hughes said: "Victor has done really well ever since he came to the club (on loan for the season from Chelsea over the summer) and it is good for him to get his first goal for us."
Hughes was also happy with the contribution of Bojan Krkic, who was making his first Premier League start since September
"I think he benefitted from the game he had on Wednesday (a start in the Capital One Cup against Southampton)," said Hughes, whose team are 12th in the table.
"I thought it was important I gave him confidence and trust today.
"You could see the difference in his play from when he started the initial couple of games at the beginning of the season.
"The more games he plays, the better he will be
He will be a success here."
Source : PA
Source: PA