All four of Southampton's players who featured in England's midweek win over Denmark starred as they overcame a battling Palace side in south London.
Mauricio Pochettino's men enjoyed 70 per cent of possession for the majority of the first half and it paid dividends just before the break.
Jay Rodriguez beat Palace goalkeeper Julian Speroni in a 50-50 challenge before sliding home the only goal of the game and Lallana admits there is no more pleasing way to end the week.
"It's been a great week," the Saints captain told Sky Sports.
"Obviously, a good win in the week but back to business at club level and I thought we showed great resilience in that second half.
"It's a tough place to come, they're fighting for their lives and it's great to keep a clean sheet."
After a fine touch left two defenders in Rodriguez's wake, the England international beat Speroni before rolling the ball into an open net from outside the area.
"He showed great commitment in the tackle with Speroni but I thought we had a couple of good chances in the first half," Lallana added.
"Rickie [Lambert] hit the post but it was going to be one of those games where they just keep putting the ball up into dangerous areas."
Palace came to the fore in the second half but failed to use a series of set-pieces as Southampton kept a clean sheet and moved within a point of eighth-placed Newcastle, although the Magpies have a game in hand.
Lallana was delighted by his side's defensive display and believes there is no reason they cannot overtake more clubs in the Premier League run-in.
"We showed great character and resilience to hold in there and I thought we fully deserved the points," he said.
"We want to finish above Newcastle, above United and if we keep performing like that and showing such character there is no reason we can't."