Lambert admitted his side had thrown away a golden chance to reach Wembley.
He said: "I am absolutely gutted, disappointed, hurt, everything.
"Everyone is hurt. You will never have a better chance to get to a cup final throughout your whole career, even the young lads.
"It may take them 10 or 12 years to get even close to one again. That's the hurt.
"I am every bit as hurt as what the fans are. It's my responsibility. I know exactly what it's like and I know exactly what they're feeling because I am feeling the exact same."