Downing celebrated his ?5million move from Liverpool with a lively 20-minute cameo as goals from Joe Cole and Kevin Nolan gave the Hammers a comfortable start to the season.
"There's no need to ask Stewart if he can prove himself because he's already done that. He's a top quality Premier League player and has been for a number of years," Allardyce said.
"We didn't start him because he was short of match time during pre-season. Cardiff were tiring and the spaces were getting wider, so off he went.
"What he contributed was exciting and he's glad to be here, that's the most important thing. We hope he gave the crowd a look at something they'll see all season."
West Ham keeper Jussi Jaaskelainen barely had a save to make all match as Cardiff endured a challenging start to life in the Premier League with substitute Nicky Maynard skying their only real chance over the crossbar.
"We've done a great job today. Our time spent in pre-season has stood us in good stead," Allardyce said. "We showed today that physically and mentally we were 100 per cent ready for the Premier League.
"We won the came comfortably, perhaps not taking as many chances as we'd have liked, but that doesn't matter now because it's a 2-0 victory and a clean sheet.
"They were two very good goals from Joe Cole and Kevin Nolan and the team performed very, very well."
Allardyce ruled out making any further signings in the transfer market, stating his budget had been spent, and revealed that Andy Carroll would also miss Saturday's trip to Newcastle with his heel problem.