Czech Republic Under-21 goalkeeper excited by run
The Hammers fell behind to Kenwyne Jones' early header but battled back superbly through goals from Scott Parker, Manuel da Costa and Victor Obinna to seal victory after extra time.
The Czech Republic Under-21 goalkeeper impressed during the game, showing safe handling and good decision-making under Stoke's trademark barrage of free-kicks, corners and long throws.
Having reached the quarter-finals and maintained his 100 per cent success rate as Hammers goalkeeper, Stech is now eyeing a favourable draw for the next round.
He told the club's official website: "It was brilliant. I enjoyed it so much. The lads did well and we all worked hard.
“We were 1-0 down after seven minutes and were a little bit down after that, but we pushed ourselves and we passed the ball well.
“It was brilliant because we worked as a team and that's what we needed to do.
"We needed to improve and we did that. We passed the ball quickly and made lots of chances and finally we won in extra time. It's great to be in the next round and I'm looking forward to it.
"I wish we'd get Wigan or West Brom. Obviously Man U and Arsenal are still in, so we will see if we have to deal with them. That's another game next month, so we'll see what's going to happen."
Wednesday's tie saw Stech come up against Potters throw-in expert Rory Delap for the first time in his career.
Stoke put a player in front of the goalkeeper in an attempt to prevent him reaching the ball, but both the 20-year-old and his defenders stood firm, punching, heading and hacking the ball clear of danger.
The stopper was happy with how he and his defenders dealt with the situation.
"When he throws the ball, everyone piles into the box and it's always difficult to deal with. There were a few crosses and throws that I came to punch away," he said.
“You can't catch them really because there are people standing in front of you and behind you - they are everywhere - so you have to get a hand there and push it away.
"The defenders did brilliantly because they came for the crosses and headed them away, so I was pleased with that."