While considerable progress was made last term, not least a 13 point increase on the previous seasonal total, the skipper strongly believes there is scope for further points gathering as the team develops.
"If you look at some of the games in the season, ones like Sunderland, Fulham and Chelsea for example, they were games when we lost points in the last minute," he reflected.
"If you were to tally up those points we would have obviously had fourth place bagged. I'm sure every team can say something that though, you've got to take the rough with the smooth and keep battling.
"Next season will be a bigger test for us now, teams know that we've got a good side and we've got to do it again," he continued, before adding that room for improvement in the group of players he regards as a positive.
"We have got a lot of room to improve and that is a good thing. People are wondering where it can lead to, but we will take it one season at a time and hope we can fulfil our potential.
"Who knows where we can get to?"
Ledley King said the team can make significant improvements over the course of next season.