I have sent out my resume to different companies, and on the reference part I did not include my reference's phone number to avoid fraudsters. Instead I put in place "available on request".
Is this practice acceptable? Will the companies I've applied to think that am not a serious candidate?
Available upon request is accepted practice, and these days it's the wiser move.
Including references on CVs or Resumes at all, however is falling out of favor. You may want to ask about this practice in your industry to see if you should continue, or simply remove them or substitute "References available upon request" in it's place.
Your references are doing you a favor. You should be doing your best to minimize the impact on them. If I found out that somebody who asked me to be a reference was handing out my phone number (even worse than my email address!) willy-nilly, I would tell that person to knock it off or lose me as a reference. Your references agreed to talk with the few companies where you've advanced far enough to be under serious consideration, not everybody. They entrusted their information to you and didn't agree to have it posted on company intranets or passed around among all your interviewers.
In my experience (high tech sector in the US), you don't even need to offer. I haven't had the once-ubiquitous "references available upon request" on my resume in at least 25 years. Of course I have references; doesn't everybody? Of course I'll provide them when asked! At my most recent interview, I had draft email waiting on my phone so that if they asked during the interview, I could provide instant gratification. (They didn't ask until later, but I was prepared.) At earlier ones (before smartphones) I had printed lists available to hand to the HR person when requested.
Your resume should be a tightly-edited presentation of the most important things your prospective employer needs to know about you. Don't clutter it up with trite boilerplate that doesn't tell them anything. And, to go back to your original question, don't be cavalier with other people's personal information if you want to keep them as references; when companies are ready for it, they'll ask.
I think that doing that is fine.
You could also consider asking each specific reference what would they prefer, so you know if it is ok to include their number or if it's better to leave it out and give it upon request like you did.
An alternative would be to list an email address or similar where possible recruiters can reach your references, which is less "invasive" than giving out phone numbers.
Is this practice acceptable?
Typically this information is provided once an offer is extended or right before an offer is extended, upon request as you stated. Base on my experience, you are following best practices.
Will the companies I've applied to think that am not a serious candidate?
This is hard to say what other companies think, but as a hiring manager, your resume would be the first I have seen with the information included up front if you decided to go that route. Don't.
