The home side went behind to an Andy Carroll header early on but responded with two strikes from Peter Odemwingie and one from Marko Arnautovic.
Speaking to Sky Sports after the game, Hughes admitted that he was pleased with the result but had hoped his side might have started better.
He said: "It was frustrating because we talked all week about the threat at set-pieces.
"But we showed character and I thought we were excellent in the end.
"We stood up to West Ham United in the second half man for man and you knew at some point we would get a chance or two.
"It's a huge three points, we're tenth in the league and looking good."
With the game level at 1-1, West Ham thought they might have had a penalty when Marc Muniesa appeared to handle in the box with Carroll challenging.
Hughes thought the referee got the decision correct by not pointing to the spot, adding: "I don't think he knew much about it. He challenged Andy Carroll and you could argue he was impeded too.
"Either way, I don't think we'd have lost anyway."
Stephen Ireland picked up the man-of-the match award and his performance came as no surprise to Hughes.
Hughes added: "I thought he was excellent from start to finish and it's frustrating he didn't get on the score sheet.
"I know what quality he has and he's doing really well."
Stoke travel to Aston Villa next weekend in the Premier League.