There are some stories where backstory is extremely important; there are some where it's entirely inconsequential.
The easy answer is: If you know what kind of story you're telling, you know whether backstory is important or not.
To take a few simple examples, in a light adventure, or a police procedural, you probably don't need anything more than establishing everybody's current role in the ensemble. In a family melodrama, it's practically a given that everybody is keying off of patterns and history that have been building up gradually.
But you could have a light adventure where the team is pursued by their old enemies, and you could have a melodrama with no backstory, e.g. about a sudden change that came out of nowhere. In many ways, backstory is a tool in your toolbox. Usually you use it by choice, because you've chosen to write something involving history and long-term developments.
On the other hand, there are also times where backstory feels absolutely necessary - because everybody has a history; because a person's history affects his life; because there's some element that doesn't make sense without a backstory explanation. Points can come up in a story where you feel like backstory is required, and if it isn't there, that can simply feel false.
And there's a case in the middle. Where there's no direct demand for backstory, but there's still a vague sense that backstory should be there. Because if nobody has any backstory, the characters might feel unmoored, living in their own little plot-bubble and having no substance to them that doesn't directly affect the story.
In other words, the problem in this middle case isn't the lack of backstory. It's that the characters seem poorly developed, or that the story feels too self-contained and artificial. Backstory is one tool to help solve that problem.
So, the questions you can ask yourself (or your critic, or additional beta readers) are:
- What backstory do I need?
- What role does backstory play in my piece?
- What are the backstory details that I want to make sure the story gets across?
- What backstory am I missing?
- Are there points in my story where backstory seems called for, but isn't provided?
- Do I have issues where backstory would help?
- Are my characters well-developed?
- Does my story feel vivid, rich in detail?
- Does my story feel artificial, constructed, with everything working out conveniently for the story?
As a broader point, when receiving criticism, I think it's always important to differentiate between comments going "This bothered me" and comments going "Here's how you should fix it."
So if your critic's comment is "There's not enough backstory," that's unfortunately a little unhelpful - backstory is a tool or a solution, not a universal requirement.
You're in one of two situations.
One is that your critic had something that bothered her, and she translated that into a "You need backstory" solution. In this case you'd ideally like to find out what was actually bugging her so you can fix that; maybe with backstory and maybe not.
The other is that your critic has adopted an "Every story needs backstory" guideline, in which case, well, she's probably off-base, applying a rule indiscriminately without being able to justify why that would be a good change to make.
Best of all is if you can ask her outright if she can explain what the problem is that backstory can solve. You might get a really helpful answer. Second best is, get more opinions - if this criticism, or associated issues, are repeated by others, you'll know you've got a problem and you'll have a better idea of the specifics; if they aren't, then it's just this one person's taste and you don't need to worry about it.
All the best!