The former Liverpool man says that the Hammers have been unlucky this season but must improve to stay up and feels that the veteran manager can help them beat the drop
The Hammers have not tasted victory in the Premier League since November and their winless run has seen them drop into the relegation places, just a point above bottom side Sunderland.
However, Downing has given his full backing to Allardyce and urged his side to improve and start picking up wins.
"The manager picks the team but it's up to us to go out and get results and that's what we've not done," the winger told reporters.
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"If you look at it as a whole, we've been very unlucky. It's up to us. The manager picks the team but it's up to us to get the results.
"We love playing for him. The owners know, they see sense and see a good manager. It's easy to sulk and point and blame but you've got to go out and get results."
Downing believes that Allardyce's experience will be vital as the Hammers battle to beat relegation from the Premier League.
"The main thing at the minute is to win games. Behind closed doors we stay strong," he added. "We are playing for a really good manager who has been in these situations before. No one wants to be relegated on their CV.
"I've been through that before with my hometown team [Middlesbrough] and it's difficult, you're living in the area and people are asking questions all the time. But we were a young team [and], when I look at this team, it's a lot stronger, with more experienced players."