His Spurs team dominated the game with 68% possession but the hosts created almost as many chances in an end-to-end encounter that had fans on the edge of their seats as the London rivals did battle in the pouring rain at the London Stadium.
"The players are showing a real willingness to learn," the Australian said of a Spurs team that were thrashed 3-0 at Fulham in their last away game. "I thought today against a tough opponent their play was quite mature.
"I'm always looking for a performance that shows we’re developing. I thought it was, better than Fulham, a similar type of game (that) didn’t handle well.
"Tonight, especially in our general play and organisation, I thought Biss (midfielder Yves Bissouma) was outstanding and the back four handled four players who will cause any team problems.
"I thought there was more structural maturity than against Fulham. We want to win but there's enough to say that it's a team still heading in the right direction."
Tottenham are battling for a place in the top four and Champions League football although Postecoglou prefers to focus on the development of his side rather than where they finish the season. They are two points behind fourth-placed Aston Villa.
Brennan Johnson gave Spurs an early lead and they could have scored through Pedro Porro and captain Son Heung-min but Kurt Zouma equalised with an effort off his back after 19 minutes from a corner and that gave West Ham more heart for the fight.
"We obviously conceded from a set piece but we still handled the rest of the set pieces really well, considering they're a big side and the delivery," added Postecoglou.
"Just probably for us in their final third, we lacked a little clarity in thought, in our decision-making.
"We got in some good areas and probably could have got some much better outcomes. I thought our general play was really good and I was really happy with it."
Tottenham face even more difficult challenges in the run-in with games against title contenders Arsenal, Manchester City and Liverpool but Villa also have to play the top three so the race for the fourth spot is likely to go down to the wire.
