The Senegal striker made it five goals in as many appearances for his new club when wrapping up a 2-0 Premier League win over QPR on Sunday with a close-range header, after Nedum Onuoha had scored in his own net early on.
Allardyce said of the former Metz forward: "I saw him as a player that, in his first season, coming in from the French second division, even though he scored 20 goals there, maybe playing 10 or 15 games for us while he found out the quality of the Premier League.
"But he's so determined to do well, his work-rate is so good and his runs are so threatening, that he seems to turn up in the right place at the right time and he has the knack.
"That's the biggest knack of all when you pop up in the right area and get the ball in the back of the net, so it's a fantastic start for him and outstanding business for us all here at west Ham."
Ecuador World Cup sensation Enner Valencia has yet to make the same impact, but Allardyce is also happy with his progress as West Ham look to be more creative up front this term.
"It's all about whether you have goal threats. If you struggle in that department, then the rest of the team comes under pressure and cracks," added the manager.
"It makes so much difference when you have a goalscorer in your team. When you look at the difference Diego Costa has made at Chelsea and we might have found two - with Sakho at the moment and hopefully Valencia might be another one.
"That's without [the injured] Andy Carroll back, so our goal threat is greater and puts more pressure on the opposition team."
Allardyce named Stewart Downing as his man of the match against QPR, but is impressed with how quickly his new recruits have settled in and hailed the team spirit instilled by club skipper Kevin Nolan.
"The captain always builds the bonds in the dressing room. We all feel together and they've hit the ground running, which is quite unusual," commented Allardyce.
"If you've got one, or maybe two doing the business, particularly from abroad, you're very satisfied, but all of them are doing well.
"The strength in depth of the squad was also tested as we had seven players out injured, but the lads have really stepped up and given a very good performance."
Get the best features, fun and footballing frolics straight to your inbox every week.
Thank you for signing up to Four Four Two. You will receive a verification email shortly.
There was a problem. Please refresh the page and try again.