Leading 18-13 with two minutes left, replacement scrumhalf Pedro Lucas gave away a needless penalty that allowed Georgia to equalise, before Portugal's Nuno Sousa Guedes missed a kick with the final play of the game to win it.
"Of course we are happy with the result, but not happy with the performance itself," Appleton told reporters. "But I think we have really built a base for the future, especially next week (when Portugal play Australia).
"We made too many mistakes, we had many opportunities to win the game, we need to work a bit more."
Portugal are at their first World Cup since 2007, and their second overall, and Appleton hopes entertaining games such as this one will inspire a new generation to take up the oval ball in a country where soccer reigns supreme.
"We want young kids to start to play rugby, to have a team they can follow. In the next few years we want to have a great team and be on top of the world," he said.
Coach Patrice Lagisquet had hoped there would be a repeat of the scenes when Portugal qualified for the World Cup as scrumhalf Samuel Marques landed a penalty with the last kick of the game against the United States to send his side to France.
"Yes, I would have liked for it to be the same as in Dubai," he said. "But with the first half (display), the result is a good one for us."
Portugal had trailed 13-0 after half an hour but rallied to lead 18-13 going into the final two minutes, only to allow Georgia to scramble a draw.
"The first half was so poor," Lagisquet said. "We were making mistakes in the lineout and we weren't disciplined. At halftime we were lucky they led by eight points and we are still in it.
"We can't have such a bad half, let's play your rugby. Be yourself."
