Pompey held Chelsea after Juan Mata netted the Blues' first goal, and Appleton insists that they had Chelsea worried.
"We got back into the game and there was some nervousness before they got the second goal. That's credit to the boys," Appleton said.
"But that's why Chelsea are in the Premier League and we are in the Championship."
Appleton also pleaded for stability at the club, and urged new owners to take control quickly this month.
"We're in the first week of January and it's important to get a bit of stability in the club," he said.
"It's a perfect opportunity for new owners to come in and really stamp their authority on the club."
Portsmouth are currently 17th in the Championship with 31 points from 24 games.