The hosts found themselves two goals down after 33 minutes at Upton Park thanks to goals from Yohan Cabaye and Loic Remy.
While a Mike Williamson own goal gave Allardyce hope, Cabaye ended any chance of a comeback with a free-kick late on, as West Ham slipped back into the relegation zone.
They had climbed out of the bottom three after last week's victory at Cardiff and Allardyce felt poor defending cost his side the chance of recording back-to-back Premier League victories for the first time this season.
"It's very disappointing, having got three points away from home (at Cardiff), that we haven't got anything here," he said.
"From our point of view it was more about defensive lapses rather than the quality of Newcastle's play, even though they are two good finishes.
"We could have done better. The fighting spirit and the fightback was there but I was thinking, 'come on lads, do a Sunderland for me', because they fought back from two goals down (against Southampton earlier on Saturday).
"But chances were there and we missed them."
Allardyce recognises the urgency of the side's current plight but told his players to stay positive.
"We keep our chins up because we've got 16 games to go and we know how many points we need to be safe in the Barclays Premier League," he added.
"We've got to keep fighting on. There comes a time where the players have to realise it doesn't become about performances anymore, it becomes about results more than anything.
"However which way you get them, you have to get them and I think that starts with us getting (back) some of the players that are suspended and injured.
"If we can get any additions, which we've been trying desperately hard to do, we will do."
'Obviously Messi is the best player in history and being compared to him means that you're doing things right, but I try to be myself': Barcelona star responds to comparisons with Argentine legend
'Darwin Nunez would be gold for Arsenal': Liverpool legend claims Gunners should have signed Uruguayan striker in January
