Tottenham would have moved above Aston Villa into fourth place in the standings with a win, but the defeat ensured Postecoglou's side remained in fifth with 53 points from 28 games.
Asked if Tottenham could still finish fourth and secure the final Champions League qualifying spot, the Australian told reporters: "I don't see fourth as the prize. I don't want to finish fourth if we haven't grown and developed as a team.
"Part of the narrative is to push you in these kinds of positions where you think that fourth is some kind of achievement that gives you something for next year.
"Fourth would be great if I feel like we're growing as a team, and we're creating something that is going to bring us success next year.
"But fourth is not our goal. If we finish fifth, and if I think we've got a team to challenge next year, then I won't be disappointed."
Tottenham next host 18th-placed Luton Town in a league game on March 30th.
