The United States international hit out at the Old Trafford club during an interview with the BBC earlier this week.
Rapinoe stated: "It's 2020. How long has the Premier League been around? And we're only just seeing a club like Manchester United put effort and pounds towards a women's team. Frankly, it's disgraceful."
Stoney, ahead of Saturday's derby with Manchester City, questioned the timing of the World Cup winner's comments and defended the actions of her club, who were only formed in May 2018 after 13 years without a senior side.
The former England and Great Britain captain said: "She is two years too late for the comments to be honest, but people will have their say. It is a big club, when you go to Manchester United you get used to that. It is water off a duck's back to me.
"I came in and everyone criticised Manchester United for not having a women's team, but I know the reasons why, I know why they wanted to do it, when they wanted to do it and how they wanted to do it properly.
"It wasn't resourced in terms of staff at the club beforehand to be done the way it is now and I believe we are in a good place and doing things the right way. We are growing slowly despite our quick progress and I am immensely proud to be a part of this football club."
• Read more: Megan Rapinoe hits out at Manchester United
Since their formation, United have secured promotion to the Women's Super League, finished fourth in their debut top-flight campaign and are now leaders of the division after six games of this season.
A 1-0 win over Arsenal last weekend showed the progress the team have made under Casey and the next challenge is a derby encounter with City.
United started life in the WSL with a clash at the Etihad in front of 31,213 spectators on the first day of the 2019-2020 season and the 1-0 loss proved to the 38-year-old her players were capable of handling life in the big league.
"It was our first ever game in the Super League, we got put at the Etihad in front of 32,000 and we did amazingly well," Stoney added.
"I knew from that moment we could compete in the Super League so it was a really good gauge of where we were at."
The Manchester derby on Saturday will kick start 'Women's Football Weekend' with top-flight matches and those in the second tier scheduled at staggered times to give the sport the best possible chance of exposure.
Arsenal's match with Chelsea is the other key fixture across the weekend, but a big absence from these games will be no supporters with all fixtures behind closed doors due to the coronavirus pandemic.
For United captain Katie Zelem, it will be a bitter pill to swallow for one member of her family.
She said: "My dad actually said 'do you think I'll be allowed to be a steward on Saturday?' because he's really missing coming.
"He literally doesn't miss a game, home or away, no matter where it is, but luckily he can watch it on TV.
"We'd love to have our families and friends in the stand, but we understand the situation is more important. We want to do them proud and hopefully everyone can be watching and cheering us on from home."
Even though the magnitude of the fixture will not be lost on anyone, especially childhood Red Devils fan Zelem, the squad have had it drummed into them it is just another match after an eye-catching performance against Arsenal.
Zelem admitted: "I think Casey will let us celebrate when we have a league title in our hands. She always wants the best for us, high standards, and she doesn't want us to get carried away too soon."
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