The Magpies had a good chance to reach their first semi-final in the competition since 1976 but were beaten 1-0 by Brentford and Bruce was left frustrated by his team's failure to take the opportunity.
He told Sky Sports: "I'm hugely disappointed that we missed a wonderful opportunity to take this club to a semi-final, where it hasn't been for 40-odd years.
"But we simply haven't played well enough to win the tie. We should have had enough, that's why I went as strong as we did. Unfortunately we haven't played well enough.
"We were too slow in possession, we didn't do enough, we didn't cause them enough problems, especially with the attacking players we had on the pitch. So we have to accept what's coming our way."
Bruce admits that he will have to bear the brunt of criticism from supporters and admits it is "fully justified" after the disappointing result.
He said: "There's no one more disappointed than me at the way we performed. I'm as frustrated, disappointed and bitterly upset as the huge following we have.
"I have to accept the criticism, which is fully justified, get ready for the challenge of a difficult Christmas period, dust ourselves down and get on with it.
"Are the players playing for me? I think they are. Maybe they're not playing well enough, but it's not without effort and determination."