Jurgen Klopp fumed at Liverpool's failure to turn a "dominant" performance into three points as Burnley escaped from Anfield with a 1-1 Premier League draw.
The visitors faced 35 shots and yet managed to hold on for a point after Mohamed Salah cancelled out Scott Arfield's surprise opener on Saturday.
Liverpool were similarly profligate in Wednesday's 2-2 Champions League draw with Sevilla and Klopp was again left frustrated by his side's inability to convert chances.
Dominic Solanke hit the crossbar late on, but Klopp felt a penalty could have been awarded when Salah went down in the box just before that.
"I'm not happy. I'm angry with the result, but pleased with the performance," said the Reds boss in quotes reported by BBC Sport.
"It's our fault. We were dominant, fantastic attitude. We played good, were fluent with seven changes. But only one goal.
"When you have shots on goal it's not about their defending. Their keeper [Nick Pope] made a few outstanding saves. I'm not happy as when Solanke hit the bar I am sure it was a penalty.
"It's the best we have played against Burnley since I have been in. In the past we didn't feel good in the game. Today I saw fluid movements, passing between the lines, speed, crosses.
"We have to take the point and carry on. "
Philippe Coutinho returned to make his first Premier League appearance of the season after submitting a transfer request in August, but the Barcelona target's numerous wayward efforts summed up the hosts' day.
Despite that, Klopp was pleased with the Brazilian's outing, which saw him get a positive reception, having come off the bench to a similarly warm welcome in midweek.
"Philippe had a really good game," added Klopp. "He had a little cramp at the end. We did not plan to take him off, but we had to decide differently."
Burnley boss Sean Dyche felt his side's direct approach had paid dividends, with the Clarets adding another impressive away result to their collection this season after winning at Chelsea and drawing at Tottenham.
He said: "I'm not afraid to get the ball forward and I thought that was effective. Our shape was good and Popey was excellent in goal.
"We know it's tough coming to these places and we are willing to do the bits that are nitty gritty in the game. Very few teams will come here and dominate, we knew we would have to do the basics. Now and again you need a bit of luck.
"We are still learning a little bit, me included, but I'm very pleased."
