The Clarets boss believed his side missed an opportunity at the London Stadium as the Hammers drew level with them on 10 points towards the bottom of Premier League table.
Burnley had led through a Zian Flemming goal but Callum Wilson, Tomas Soucek and Kyle Walker-Peters all replied for the hosts before Josh Cullen pulled one back with the final kick of the game.
“We’re angry and disappointed,” said Parker. “We feel like we’ve let one slip.
“For 30 minutes we were excellent and deservedly went a goal up. We nullified any of their threats and we were well on top.
“But from the moment we scored, we lost focus and turned it into a basketball match, end to end, which suited them more than it did us.
“We fell short from a set play just before half time and that gave them an avenue back into the game.”
Parker felt his side started the second period as well as they did the first, but the impetus changed when the Clarets conceded a ‘soft’ second.
“In crucial moments, there was a lack of concentration. We fell a bit short in certain moments,” he said.
“There were nice bits in the second half again, but we gave them another poor goal.
“We lacked a bit of nous in those moments.
“There’s stuff that is costing us at the moment and it’s up to us to fix those things.
“We’re all leaving here thinking we’ve missed an opportunity - that’s the big frustration.”
The defeat, which follows last weekend’s 2-0 home defeat to Arsenal, leaves Burnley out of the bottom three on goal difference.
“I don’t know whether it’s harsh,” said Parker. “My feeling is we were exceptional at start of the game, showed maturity, quality, got our noses in front with a well-worked goal.
“But then we played the game the way West Ham wanted. A basketball match, counter-attacks, wide open spaces, and we switched off.
“If you switch off for one second there’s every chance the ball will end up in your net. It’s something we’ve got to fix.
“I can praise how well we did and what a good side we looked but we’re coming away with a loss. This is a big league, a big man league and we need to learn from that quickly. It’s a massive opportunity missed.”