However, Shakespeare said that benchmark could be misleading.
"I don't know the average for this season and that is the problem. We don't know because we don't know how many points the other teams are going to get," Shakespeare, whose side have earned 16 points in seven games since he took over in February, told British media.
"If the other teams go on a run we have to put as many points on the board as we can... All I am concentrating on is making sure I stay focussed and the players stay focussed, and try to win every game we are in."
Leicester have a tough run-in with games against Arsenal, Manchester City and Tottenham Hotspur in their remaining league matches.
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Palace is the only team from the bottom half of the table set to face more top six clubs than Leicester before the season ends and Shakespeare is wary of slipping into the relegation zone.
Shakespeare defended his decision to field a strong side against Palace despite Tuesday's Champions League quarter-final second leg against Atletico Madrid.
"We needed to be competitive and we had to pick a team to do that. I am not sure how many points it will be for survival so we had to be sure the team we selected was coming here to get a result," Shakespeare said.
Leicester's next league match is against Arsenal on April 26.
(Reporting by Aditi Prakash in Bengaluru, editing by Pritha Sarkar)
