Fonte headed home his second of the game at the death after the visitors had recovered from going behind in the fourth minute to lead.
Jos Hooiveld's own goal made it 1-1 before Kieran Richardson put the Cottagers in front with two minutes to go.
"(We're) a bit disappointed, we were in front for quite a lot of the game, but to come back in the last two minutes and salvage a point is credit to the lads," Lallana said.
The point was only Southampton's fourth from seven Premier League games this term and Lallana knows they have to improve at the back.
"For a lot of us it's our first season in the top flight, we've got to learn fast and got to keep clean sheets, because that's the only way you're going to get points," he said.
The brace marked Fonte's first Premier League goals and he said: "It was good to get two goals, but at the end of the day the most important thing is the team."