Sunderland, who are preparing to face Bolton tomorrow night in the replay at the Stadium of Light, came from two goals down to draw 2-2 against the Trotters, knowing a tie against Everton was at stake.
The Black Cats then took the fighting spirit from the second half at the Reebok Stadium and used it to brush aside West Ham in their Barclays Premier League clash on Wearside last weekend.
The three points helped to ease their relegation fears and O'Neill was quick to laud the spirit shown against Bolton as the catalyst for the much-improved performance.
"The difference between our performance against West Ham and Bolton was obviously day and night," O'Neill told reporters.
"We started sluggishly against Bolton and I don't think we can afford to do that, but against West Ham we started strongly and the most pleasing aspect for me was that we kept it going.
"For the most part, we were terrific.
"Our second-half performance against Bolton in the cup helped cement that. It gave us that lift, not only that we were still in the cup but the players felt that now they could move on."