In the end, it was FA Cup holders Chelsea who progressed into the last 16 following a 2-1 victory at the JJB Stadium.
Chelsea should then have seen the game out, but substitute Antoine Sibierski scored a stunning 87th-minute volley, while Marcus Bent came close to forcing an unlikely replay as he struck the crossbar in injury time.
Bruce, though, was left to lament Anelka's strike as he said: "It is down to individual error.
"For me we had a chance in this cup tie, and it was never going to be a classic because of the state of the pitch. Both sets of players have done their best to make it a cup tie because it is difficult. But if we've intentionally tried to play offside then we are at fault. You can't take a risk when you've somebody like Anelka.
"That's why he has cost so much money. He is always playing off your shoulder, and that's the one thing we talked about for three days. For me it should be bread and butter. We should be picking him up, and while the kid (Juliano Belletti) has played a good pass, it's cost us the game."
Blues boss Avram Grant insisted the rutted pitch "should not be allowed for a Premier League club," yet heavy rain in recent weeks has resulted in its present atrocious state.
"The pitch is what it is, and there's nothing I can do about it," added Bruce.
He then joked: "It should improve in a fortnight when the rugby boys (Wigan Warriors) start playing on it! That will do it the world of good.
"But we have to get on with it, and I'm not going to make it an excuse."
Grant's side may again have been without nine key players, but they are now unbeaten in their last 10 matches and remain in the hunt in all four competitions.
Anelka will certainly aid the Blues cause, with Grant stating: "He is a proven striker, and I think my judgment on him has proven to be correct, and not just because of this game.
"But the most important thing is we keep the style of the team, even if we've a number of players unavailable. The likes of Shaun Wright-Phillips and Steve Sidwell are doing a decent job, and that tells me what I thought, that the players have developed well in the last three months.
"We have developed our football, our spirit, and we keep playing our game, even on a pitch that is not good enough for the Premier League."