Spurs won five of their last nine Premier League games and prematch coach Jose Mourinho bemoaned the end of the season as it comes when his side have found form.
"My feeling is, in normal conditions, we would fill the top four without problems and we probably wouldn't need more than a couple more matches to do that," he said.
Jeffrey Schlupp had Palace back on level terms eight minutes after half-time following poor defending from Tottenham at a corner.
Spurs were 14th when Mourinho took over from Mauricio Pochettino in November and he has overseen a marked improvement in form despite injuries to key players, including Kane and Dele Alli.
"When we are all ready, we can be a very strong team," Mourinho added. "When we have certain principles of play very automatic, we can have a very, very strong competitive base and we look forward to next season."
Wolves' 2-0 loss at Chelsea ensured a point was enough for Mourinho's side who ended the season on 59 points, above Wolves on goal difference, thanks to a strong finish to a season of upheaval at the club.