The Hammers face a trip to Merseyside to take on a side that has struggled so far this season having lost each of their last four league games, the latest being a 2-0 defeat to Hull City yesterday.
But with a different competition it could represent a break from the troubles of their Premier League form for Roberto Martinez, and it is something Downing is wary of.
He told the West Ham website: "It's a big game for us on Tuesday. Everyone wants to do well and progress and we'll have a couple of days rest before getting back to normal week-to-week football.
"I'm not sure if it's a good time to be playing them. Everton is always a difficult place to go, no matter how they're doing. They play some great football and it's only one result around the corner from them kicking on and we don't want to be that team.
"We were unlucky in the league there so we owe them one."
West Ham will be looking to bounce back from a disappointing 1-1 draw in the Premier League against West Bromwich Albion, whilst Martinez will look to perform the same kind of heroics that led Wigan Athletic to the trophy in 2013 - though he would hope their league form takes a turn for the better soon.
Though Everton are in poor form, they are a side that seems to play well against the bigger teams, and if they lose out it tends to be by the odd goal, very rarely do you see them get comprehensively beaten.
Downing is therefore right to warn his teammates about any potential backlash he and his teammates may face.