Why are you letting Sheldon Cooper proofread your stuff? Sarcasm normally sounds somewhat mean, but you can prevent it from sounding serious by saying something that you obviously wouldn't believe. Make it obviously factually incorrect or something like that. In some cases it may be more tricky and I'd have to see exactly what you're writing.
I have the opposite problem. Whenever I say something serious people believe I am being sarcastic. And I am not. Heck, I am not even entirely sure what it means to be sarcastic, outside of the definition in the dictionary which still leaves me mystified. Good luck in finding an answer. Lots of knowledgeable peeps on this site so there's good likelihood of it.
Actually, what I said is just part of it. Even if it's obviously not literally true it could sound like your true feelings. If you're sarcastic about something that's not a sensitive subject, with a friend that you've been having a fun, casual chat with for the last 30 minutes, then you say something sarcastic that's obviously not literal and a little off the wall, it could work.
Did readers indicate that they weren't able to tell if the comments were sarcastic? Or are you just suspicious?
I tend to run a bit sarcastic when I'm not careful. It's a trait that people who know me well and are familiar with how I think and speak take pause when they detect it and double check. It's nuanced - I guess some people are overt about it and they come off as total jerks, but most people don't seem that way to me. Long story short, I think it will take a while for your reader, and for the characters they talk with, to figure it out as well.
No one has ever said anything (because I haven't shown anyone yet), it's kind of just a feeling a get. I mean, my work isn't riddled with sarcasm, but it is present in the dialogue on occasion. I think it's usually obvious enough for people to tell it's sarcasm, but it's never outright stated.
I think you might want to try letting someone read a section of your work and see what they say. Was it funny and/or sarcastic? Did that come across? Is there enough going on with the subtext of the story to know when a character is being sarcastic? Also, there is nothing wrong with a dialog tag that directly says the character is being sarcastic. Stating that something said was said sarcastically would not bother me at all. Sometimes you have to be clear and direct. I'm not saying you have to do that, only that seeing that wouldn't bother me as a reader.
The other thing is that we are often not the best judges of our own writing. Most of what I write is dark comedy, absurdist fiction and satire. I usually have a hard time deciding when something is or isn't working. With some of my works, I have been told to push it more in the comedy direction and other times that a running joke in a story is taken too far. Even if it's only a friend and not a writer friend, it can be very helpful to find out how your sarcasm is being perceived.