A total collapse from the tourists on the final day of the second Test in Adelaide handed the Aussies a 120-run win, putting them in prime position to wrestle back the urn with three matches remaining.
England have now been bowled out for 302, 185, 227 and 233 in their four innings Down Under but speaking to the media today, Bayliss was confident that his side can sill "compete".
"I don't think there is a real need to panic, the guys have shown the capabilities we have got," he is quoted as saying by the Daily Mail. "We have just got to find a way to do it for longer.
"In both Test matches we have competed for a couple of days but to win against Australia in Australia we have to compete for longer than that.
"All of our players have competed at different times and showed they can bat but we just have to do it for longer. We have to work out a way to keep that concentration and compete for longer."
The third Test gets underway in Perth on December 14.