"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.
Cardiff were making their first appearance in the top flight since 1962 and manager Malky Mackay felt they had acquitted themselves well, despite their obvious shortcomings.
"We started slowly but after that we had an awful lot of possession. We knew we were coming to a good team in a good atmosphere," Mackay said.
"They were clinical with Cole's goal and while we had plenty of possession, there was no penetration. We grew into the game in the second half.
"Overall I can't be too harsh on my players because we gave a good account of ourselves. We weren't overawed and that showed today."
Mackay revealed that new signing Andreas Cornelius will return to training next week after missing the match with an ankle problem and announced that additional recruits could be heading for Cardiff City Stadium.
"We're trying to get new players and we'll keep trying to do that, but sometimes it's not always in your control," he said. "If I find a good player and everything comes together in terms of the club and player agreeing everything, I'll absolutely try and act."
- Sports & Recreation
- Premier League
- Joe Cole
- Kevin Nolan