Luis Suarez skied an early penalty after being brought down by Kieran Richardson, but the Copa America star recovered and put Kenny Dalglish’s side ahead with a glancing header from a Charlie Adam free-kick.
However, Sunderland turned their fortunes around in the second-half and put the game back on level terms with a fantastic acrobatic volley from debutant Sebastian Larsson.
Bruce said of his team’s performance to the press: “Well we got off to the worst possible start, made it very difficult for ourselves and got away with it in the first 15, 20-minutes to be honest.
"That was a bad period but the longer the game went on, we posed more of a threat to them and we deserved to get something out of it.
“The wonder-strike from Seb [Larsson] has got us a point, but overall when you look at the context of it, I can’t really remember my goalkeeper [Mignolet] making too many saves and we’ve come away with a deserved point.”
On his team’s second-half resurgence, he added: “I think a little bit more belief. We had to keep the ball a bit better, and that we did, we did in the second-half and became a threat to Liverpool. We had one or two chances in the first-half, but didn’t keep the ball as well as we would have liked. The second-half we did much better.”
The north east native was lucky not see his defender sent off for his foul on the Uruguayan striker, but Bruce believes Phil Dowd made the right decision not to send off Richardson.
He explained: “Yes, of course you fear the worst, but I think the referee’s experience has put him in heart there that I thought, as he did Phil [Dowd], that probably we were going to retrieve the situation, I think the goalkeeper might of got there before [Luis] Suarez, I think he overran it a little bit.
“I think it’s more clumsy of Kieran [Richardson] than intentional and it could have gone a red card I suppose, but I think he’s made the right decision, but I suppose I’m going to say that. You don't want to see red cards anyway, it ruins the spectacle.”
The Black Cats' hero of the match, Larsson, was brought in from relegated side Birmingham during the summer on a free transfer and Bruce was happy to see the value he had looked upon in picking up the winger.
“Well I’m delighted we’ve got him [Larsson],” Bruce said.
“I had the good pleasure of working with him for three or four years and he’s developed as a player and as a person and we all know we needed to add something to our set-piece delivery.
“Of course he’s one of those manager’s dreams where he gets on with everything, left or right, what a way mark your debut with a spectacular goal like that.”
Forcing a point out of a strong, optimistic Liverpool side will have caused a stir at Anfield and Bruce was delighted to see his team’s season kick-off in such a positive light.
He said: "Overall, we are very pleased. We finished tenth last year so it was important for me to give a chance to the lads who served the club so well last year. I wanted to stay loyal to the lads."