"I know what my best is, and it's not here yet," said the Argentine.
"Yes, I've been happier with how I've played in the last three games, but I need to still improve.
"I feel I still need to know a lot more about my opponents and my team-mates. You never stop learning, no matter how long you've been in the game. You can improve every time you play.
"I'm not thinking about what will happen with me ahead of next season. All that's important is Liverpool win, catch Everton and finish in the top four."
"I have said many times that Pellegrino is a winner," said Benitez.
"He works hard in training and he's playing well for the first team at the moment.
"I haven't spoken to him yet about the future. I will speak with him before the end of the season about what we both want to do."
It is rumoured that Pellegrino will be offered a coaching job at Anfield when his playing career is over.