The England international played the full 90 minutes on Boxing Day as the Reds recorded a 5-0 win over the Swans at Anfield.
He was also able to get on the scoresheet, scoring the final goal of the match but the former Arsenal star claimed his display was not good enough.
Oxlade-Chamberlain originally struggled to get into the first team but has now started three of the last five matches and Klopp expects him to kick on.
"Ox is a smart player. He knew it was not even close to his best possible performance [against Swansea], but it's no problem, that's football," the German told the club's official website.
"Ox needs to adapt to the position still, that's no problem. He has a lot of space for improvement. But it's nice to see that he is really working hard on it.
"He is a really hard-working boy and wants to improve. It's good that he knows he can do better now we have to work together on it so he can do better."