The vaccine passport system was implemented in October, with Scots being asked to show proof of full vaccination through an app or paper record to access nightclubs or large events such as football matches.
The scheme was met with criticism from opposition politicians and venues that would be impacted, who railed against logistical difficulties in implementation.
Speaking before the Covid-19 recovery committee on Thursday, Mr Swinney said: “The vaccine certification scheme works well.
“I fail to understand what the fuss is about it. I think it’s a completely reasonable request for us to make.
“When you have a system in place that involves over ten million individual vaccinations, there’s bound to be teething issues on certain vaccine certificates and I’ve made it clear that ministers will help to resolve any issues.”
Mr Swinney, who is also the Covid recovery secretary, would not be drawn on any future expansion of the scheme to include more venues, something the First Minister said on Tuesday was still under consideration by ministers.