Captain Steven Gerrard said Liverpool must improve to progress in the Champions League after they needed his late penalty to beat Ludogorets 2-1.
The 2005 winners looked set to drop points against the Group B underdogs when Dani Abalo cancelled out Mario Balotelli's opener in stoppage time.
But Gerrard's spot-kick secured victory for Liverpool, who visit Basel next before a home tie against Real Madrid.
"We did OK but it wasn't better than OK," he said. "There's a lot to learn."
Gerrard acknowledged Liverpool were caused problems on the counter-attack in their first match in the Champions League since 2009.
But he praised striker Mario Balotelli after the £16m summer signing from AC Milan scored his first goal for the club against the Bulgarian champions.
With eight minutes left, the Italian controlled the ball and turned in a single movement before steering it into the net with the outside of his right foot.
Gerrard said: "You have to give Mario credit. It didn't go his way for long periods but the sign of a good goalscorer is to keep going and get a chance.
|Liverpool's Champions League journey|
|Basel (A) 1 October|
|Real Madrid (H) 22 October|
|Real Madrid (A) 4 November|
|Ludogorets (A) 26 November|
|Basel (H) 9 December|
"If we win in Basel now it puts us in a good position but we must do better."
Liverpool manager Brendan Rodgers also acknowledged his team need to recapture their best form after a patchy start to the season.
The Reds, who secured their return to the Champions League by finishing second in the Premier League in 2013-14, have lost twice in the first month of the campaign - to Manchester City and Aston Villa.
"We are not yet at the level we were last season but we will get there," said Rodgers.
"It was a great night in the end because we won.
"Ludogorets played very well. They are a very good side and to get the win was very important."