Aaron Cresswell, Cheikhou Kouyate and Mauro Zarate were among seven of Allardyce’s signings and the trio played their part in Saturday’s 3-1 win over Crystal Palace.
Zarate opened the scoring with a spectacular volley, while further goals from Downing and Carlton Cole secured a first Premier League victory of the season at Selhurst Park.
A mid-season injury crisis hampered the Hammers last season, but Downing believes there is much more strength in depth and has been impressed by recent additions.
"I think all the new signings have settled in well and those who have played have made good starts," said the winger.
"We have a bit of a stronger squad this season which I think helps the manager. Last season the team had to literally pick itself at times because of injuries.
"We have a lot more options now and can change it around a bit if needed."
The 30-year-old has slipped out of England contention, but gave a reminder of his attacking threat with a curling shot past Julian Speroni in the first half.
He admits that Allardyce has urged him to shoulder some of the goalscoring burden during this campaign.
"Obviously I am eager as is the manager for me to get more goals this season," he said.
"To get off the mark second game in, is nice. I want to shoot more, get in the positions I need to be in. With the goal, I had it in my head what I wanted to do and hit it where I wanted to and it worked."