The hosts had the better of the opening period, and took a deserved lead through Daniel Agger's header two minutes before the break.
Saints' second-half showing was more reminiscent of the performances put in during the recent run of four games without a loss, but they could not breach Pepe Reina's goal.
And, while he admitted he was disappointed to see his side's recent revival take a hit, Lallana drew positives from the team's trip to Merseyside.
"This is something for us to look up to," the skipper told Saints Player
at full time.
"The way they played out from the back and played with the ball was great, and we couldn't live with them.
"We'll take positives out of the second half because we stayed in the game and were in it right until the death so anything could have happened.
"Two months ago, we might have lost that by four or five like we did against Arsenal. We'll take something away from the game, but we're disappointed not to get anything out of it.
"That first half was tough," Adam continued. "It would have been nice to come in at nil-nil but they've scored a few minutes before half time.
"In the second half I thought we had a lot better shape about us and the game-plan worked because we sat off them a bit and let them play the ball out from the back.
"We were in the game until the end, and you never know – we could have nicked it because we had a couple of counters."
After three games in seven days, Saints' players will get a chance for rest and recuperation before they return to action next Saturday.
Our next game sees us host Reading at St Mary's, with Lallana already highlighting the important of overcoming the side that pipped Southampton to the Championship title last season.
"We now have to get ready for Reading, which is a massive game," he affirmed. "We owe them one after last year because they beat us 3-1 at St Mary's.
"We always knew this was going to be a tough week and that it was going to end with a tough game.
"We were disappointed not to win in midweek because that might have made today a bit easier and put a bit less pressure on us.
"We have shown improvements of late and we've got a big Chrismtas period coming up without a midweek game this week, so we'll recover well.
"All our eyes and focuses are on Saturday's game.
"We know we've made massive strides over the past four-or-five games, but it's important we continue that," he added. "We know how important next week's game is for taking points off teams around us.
"The way we've played in the last four games – and in the second half today, at times – shows we are very confident."