The Hammers drew 0-0 at Southampton in the Premier League on Sunday, which means they have not scored in three league games since the opening-day 2-0 win against Cardiff City.
"We're concerned that we haven't scored for a while. It's not that we're not creating chances, but our quality of finishing has to improve. We've ended up drawing two and losing one because of that," Allardyce told a press conference on Thursday, ahead of the visit of Everton to Upton Park on Saturday.
"Only conceding one in four games is a great platform but we have to take our opportunity to score when it comes.
"Everton's players are more or less the same and Roberto has made some very good additions. Barry is an outstanding signing.
"When you look at the squad as a whole, it is very strong indeed. We expect them to maybe play out of the back a little more.
"But in general, they play the same after that. They try to get into the final third and get good quality balls into the box.
"They had a fantastic result against Chelsea and we expect a very tough game on Saturday."
Allardyce was forced to make-do-and-mend for the visit to St Mary's last weekend, and there would appear to be little respite on the injury front this week.
"Andy Carroll is recovering well now. We have a programme set out for his recovery and it won't be as long as last time," he said.
"Let's see where it is week on week. He will take some time away to have some one-on-one stuff and hopefully that will speed it up.
"Petric is training every day and trying to overcome the fatigue he's feeling. He's going through pre-season work, which is more intense physically than general training.
"His recovery is getting quicker and he's coming along. He's enjoying being back in with a group. We'll expect him to be able to make an appearance against Cardiff (in the Capital One Cup tie on Tuesday). He's coming along fine.
"George McCartney is back training with us and we're very close to Joe Cole and Stewart Downing being back too, probably after this match."