The Hammers beat the Belgian side 4-1 (5-2 on aggregate) to move to the next stage.
A double from Michail Antonio and a penalty from Lucas Paqueta set the London club on their way to victory.
Declan Rice scored a superb solo goal in a thrilling second-half display.
West Ham have reached the semi-final of a European competition for the second consecutive season.
They progressed to the last four of the Europa League in 2021/22 before eventual champions Eintracht Frankfurt knocked them out.
Moyes said (via West Ham’s official website): “Look, I felt a big relief because we hadn’t played well in the first game against them.
“Losing a goal in the first half was terrible and I was thinking, ‘my goodness, this is maybe going against us tonight’.
“But we were the better team, even in the first half I thought. We got back in the game and then we missed two brilliant chances to go ahead before we got the penalty kick.
“It was a big relief when we got the third goal because it put complete daylight between us and the thought of getting to a European semi-final two years in a row with West Ham was special.
“We want to be in the final. We’re all looking forward to trying to get to Prague.”
Despite Moyes being 180 minutes away from the final, he urged caution. He is not thinking too far ahead as they have a semi-final to play against AZ Alkmaar first.
West Ham will return their attention to the Premier League this weekend. They are only four points ahead of 18th-placed Nottingham Forest and face Bournemouth on Sunday.
A victory would ease West Ham’s relegation worries and set them up nicely for their crunch European tie in May.
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