"We've always focused on the game and that won't change," said Klopp.
"We didn't come here and have the numbers we have because we thought about breaking records.
"Hopefully in the future, when the record ends or the season ends, I can start thinking about it.
"If we can do something special it is great but we really don't think too much about it."
"I don't want to be a valiant loser, we're scrapping for points," Villa boss Smith said.
"To out-shoot Liverpool at home at Anfield, in terms of efforts on goal, it's excellent - but we need to take our opportunities. We never found the quality in the final third they did."
Klopp added: "Aston Villa were fighting with all they had and it makes life uncomfortable.
"I like it, it was not a brilliant performance but it was a good performance that gets us three points."