The visitors took a two-goal half-time lead, which was a touch harsh on Sunderland, who had earlier hit the bar through Sebastian Larsson before Emanuele Giaccherini pulled a goal back in the 52nd minute.
Try as they might, the Black Cats could not find an equaliser and were undone by a counter-attack as Luis Suarez clinched victory for Liverpool in the closing stages.
"We spoke at half-time and I thought you saw a great reaction. They gave it a really good go in the second half," said Sunderland's interim head coach Ball, who was taking charge of his first Premier League match following Paolo Di Canio's sacking last weekend.
"We took it right to the death but unfortunately you're susceptible to that counter-attack where 3-1 - and I don't mean this as disrespect to Liverpool - flatters them a little bit.
"It was a shame because I thought the lads had a real good go today and that's something we need to take heart from."
The final touch for Liverpool's opening goal came from the arm of Daniel Sturridge but Ball preferred to concentrate on the defensive deficiencies of his side rather than criticise the officials.
He said: "It did come off Daniel's arm but that is one of those things and the point that I'm more interested in is that he had a lot of space and we could have done something more to prevent it happening."
Ball added: "I think you saw today a hard-working, committed performance, but there was a lot of good football in there as well and we can take heart from that.
"Lee Cattermole was excellent for the time that he lasted on the pitch again, so that bodes well for the future."