Lavia was handed a start after a long-time injury absence and impressed for 55 minutes before his substitution.
"I think we played a very good game overall," Lavia told chelseafc.com.
"Whether we deserved more, that’s difficult for me to say but I thought we created a lot of chances and controlled the game in large spells.
"Did we deserve more? For me, probably yes but that’s just my initial thoughts and we should still take heart from our performance.
"Coming to Anfield and playing such a strong side, you know that there will be times where we lose transitions and they can counter but I felt we dealt well with their threat on the whole and we created a number of opportunities of our own.
"We knew we were playing a really strong side and unfortunately they came out on top but I think there are a lot of positives we can take from this game to take for the rest of the season."
The midfielder also said: "Of course, I’m very happy with the minutes I got and it’s pleasing to be back in action and helping the team.
"I’m a competitor though and I want to win, so I’m disappointed with the result. It’s a day of mixed feelings really.
"The manager made the decision to manage my minutes and bring me off before the hour. Of course, I want to play every minute but it’s a decision he made that he felt was best for me and best for the time and I’m happy with that."