But the Hammers are enjoying a fantastic new era under Slaven Bilic after he landed the job and are officially the most improved team in all of Europe.
A memorable season has already produced a first win at Anfield for 63 years and first double over Liverpool since 1964 as well as away wins over Arsenal and Manchester City while Bilic's men have also put Chelsea to the sword at Upton Park.
Their excellent form, attacking prowess - despite missing as many as seven key first team players all at the same time recently - and new found style have made them a surprise package to challenge the top four.
'West Ham look a club on the up'
And despite the defeat at St James Park, which ended a club-record equalling eight-game unbeaten Premier League run, Moyes told BBC's Match of the Day the club has a lot to look forward to.
"West Ham have done really well, in fact they've been one of the surprises in the Premier League," Moyes said on MOTD.
"Slaven Bilic has done a great job there, I've come across him a couple of times in Croatia over the years and he was very accommodating I must say.
"He's done a good job and we must give Big Sam credit because Sam got a lot of stability into West Ham and Slaven has come in and taken them on and they've made some good signings as well.
"I think West Ham are a club who look as though they're on the up going to the new stadium as well so they've got a lot of things to look forward to."
Former Everton manager Moyes knows what it takes to build a side capable of challenging the established teams after a decade doing just that at Goodison Park.
But he is not alone in backing West Ham for bigger and better things.
Liverpool legend turned pundit Dietmar Hamann said last week that 'massive' West Ham can start to challenge for the Champions League places.
And recently London Mayor Boris Johnson described West Ham as the biggest project of their kind in Europe and tipped them to change the face of London when they move to Stratford.
"This is just the beginning," Johnson told whufc.com.
"I think people will look back, everyone involved with West Ham, everyone who supports West Ham, I think they will be very proud, actually, that they are part of something that is the biggest economic social regeneration project anywhere in Europe.
“I think West Ham fans are part of something that is going to change the face of London."