Pascal Gross and Glenn Murray struck late as the Seagulls battled back from 3-1 down to snatch a 3-3 draw last weekend.
It was the third time in their brief Premier League history that the south coast outfit had fought from two goals down to claim a share of the spoils and Potter is expecting to see more of that same fighting spirit going forward.
The Seagulls might be without a win this year, but Potter was encouraged by what he saw from his side at the London Stadium ahead of their clash with fellow strugglers Watford on Saturday.
Potter said: "It (the West Ham game) was a good point for us in terms of how we got the point. We're a little disappointed not to get the three, but to come back twice in the Premier League is a character and a determination that I think you need to show as well.
"We need to improve our points tally - that's quite fair, and obviously we're focusing on that for the weekend."
Watford had spent the majority of the season at the foot of the table but have improved in recent weeks under Nigel Pearson, who has taken them from bottom to just two points from safety since replacing Quique Sanchez Flores in early December.
Potter started his career as Brighton manager with a 3-0 win over Javi Gracia's Hornets in the first match of the season, but expects a different challenge against Pearson's men.
"Nigel has come in and steadied the ship and made use of the quality which is there - don't forget this is a team which finished in the top half of the Premier League last year, FA Cup finalists," Potter added.
Brighton are currently sitting in 15th place in the Premier League standings, just two points above the relegation zone, but also just five points behind 10th-placed Arsenal.