The 24-year-old was given his marching orders in the 17th minute of the game for an elbow on Aaron Cresswell.
However, the Croatian claimed that the 2-0 win was a massive result for the Hammers after they managed to eventually breach a Villa side who had thrown number behind the ball to deal with being a man down.
"It's a massive win for us," said Bilic after Michail Antonio and Cheikhou Kouyate scored in the second half.
"I have nothing but praise for my players, and I have to congratulate Villa's players for fighting and not giving up.
"Until the red card they were confident. Unfortunately for them that moment of madness affected the game a lot.
"In the second half we played exactly the way teams should play. We didn't panic, we were patient, dynamic and quick, but without losing composure and shape.
"We played really good. We are becoming a serious team."
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