Abion kept their first clean sheet in seven games but couldn't find a way past Clarets' keeper Nick Pope despite a Man of the Match performance by Lallana.
“It pretty much feels like a missed opportunity, we should be winning games like that at home," he said.
“We had a number of good chances and their goalkeeper made a couple of good saves, but we probably could have worked him a little bit more.
“It's frustrating and it's small margins in this league. We have got to turn the good performances into results. You can't help but look at the table and think we should have three or four more points."