This is according to Graeme Souness, who was commenting after the Hammers' stunning comeback against London rivals Tottenham on Sunday afternoon.
Spurs looked home and hosed within 16 minutes of kick-off at White Hart Lane, and Jose Mourinho even treated supporters to Gareth Bale's second debut - introducing him from the bench in the second half.
Heung-min Son scored in the first minute with Harry Kane adding a brace over the next quarter of an hour - but everything collapsed once Bale was introduced on 72 minutes.
Fabian Balbuena pulled one back to little fanfare ten minutes later, but things got tense when Davinson Sanchez headed into his own net with five minutes to go.
And with almost the final kick of the game, Manuel Lanzini netted a goal of the season contender to complete West Ham's stunning comeback and have David Moyes dancing on the pitch.
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The Hammers headed into Sunday's match with two successive wins by a combined 7-0 scoreline, and the draw in north London makes it three Premier League games without defeat.
They sit eighth in the table after five matches despite many critics believing West Ham had the hardest opening fixture list of all the 20 top-flight clubs, and right now appears a good time to be a Hammers fan.
And the east Londoners should be fighting to finish in the top six this season, Souness believes.
"After the first game of the season against Newcastle, I thought maybe they'd got their pre-season wrong because they didn't look like a team that was ready for the first game," said Souness on Sky Sports. "They looked weak, they didn't get near Newcastle; Newcastle deserved to win.
"And then we put up the list of games that were coming up and you're thinking, 'where are they going to get points from?'
"It shows you how mad football is.
"Since the first game, they've gone to another level.
"West Ham have a good group of players, a good manager and they have a really passionate support; sometimes that can be a problem if you're playing there and they get frustrated. But only because they're desperate for West Ham to do well.
"I see West Ham as a team that should be in the top six, definitely. Historically, they have not done it consistently, but they should be, they're a proper football club."
Former Liverpool defender Jamie Carragher similarly spoke highly of Moyes and admitted he hopes the manager can replicate the fine work he did while in charge of Everton.
"I really hope David Moyes does a similar job at West Ham to what he did at Everton and gets a good few years there," added Carragher. "They're similar sort of clubs, you'd class them just outside the top six.
"With the sets of supporters and traditional years of success in the past of winning trophies, David Moyes got really close to that at Everton, pushing the top four and top six at times year in, year out and that's what West Ham fans are craving for."
West Ham are a 'proper football club' who should be fighting to secure a top six finish in the Premier League.