It took the Hammers until the 112th minute to find the winner, Reece Burke slamming home a rasping half-volley to break the Salopsians hearts.
“I'm very proud", Hurst told the club's website.
“West Ham put the big guns on to try and get the victory, which eventually they did in the end, but it took a long time to break us down.
“I'm just really disappointed with the goal that's beat us. It wasn't as if Lanzini or Arnautovic picked the ball up and bent one in the top corner, it was a nothing goal.
“We didn't deal with it and then their lads got to it first and even then it's gone in off the bar, so it's a bit heart-breaking because you get to penalties and who knows.
“You'd always say that you'd fancy the team with more technical quality, which would be West Ham, but you never know.
“Often when you get beat you do have mixed feeling, especially on a night like tonight, but it was certainly a massive effort from the players and it could have been a different story I think tonight."