Latest figures show a 7% drop in the number of passengers in the year to September.
Barber, a former RAF group captain who was appointed the airport’s operations director in May 2012, took over as managing director two months ago.
This followed the Welsh government buying the airport for £52 million in March last year following concerns about a lack of investment by the previous owners.
Barber told the BBC: “It’s a tough climate for smaller airports at the moment, the economic situation has had a big impact on the situation and we’ve got to respond to that.
“We’re working really hard with the airlines to get them back in here, to get sustainable routes that we know are going to last and stay the distance.
“It’s all about making sure we offer passengers the best possible experience when they come here so that their choice is to come here rather than go across the bridge into Bristol.”
Her comments come as KLM announced it is increasing its capacity from Cardiff with a larger aircraft on flights to Amsterdam.
While more than one million people travelled from Cardiff in the last year, Bristol attracted almost 4.5 million passengers.
Sourced from Travel Weekly