The England international played just over an hour on Saturday as West Ham followed up their opening-day win over Cardiff City with a 0-0 draw against Newcastle United away from home.
But the 29-year-old, who moved to Upton Park from Liverpool earlier this month, is keen to get more minutes under his belt in the cup.
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"The squad is obviously not massive so I expect everyone will be involved and the gaffer might change around a few. For me personally, I just want to keep playing and get as fit as I can and get a good run at it.
"A lot of teams disregard the League Cup a little bit but I always think that if you go strong in it, you've got every chance.
"Certainly at Middlesbrough and Liverpool we had that and I also got to the final with Aston Villa. I think we should just go for it because a few teams do disregard it."
Downing also looked ahead to the weekend meeting with Stoke City, which he believes his side can use to cement a fine start to the new season.
"We're a little disappointed we didn't get all three points at Newcastle but getting a point is still good," he continued.
"If we can win at home next week, that point looks even better. We'll be up for it and Stoke will come and have a go at us, so I'm looking forward to it."
Downing has won the League Cup with both Middlesbrough and Liverpool during his career and was a beaten finalist with Aston Villa in 2009-10.