Boss Ralph Hasenhuttl accused Southampton of complacency after they blew a 2-0 lead at Derby.
Nathan Redmond's stunner had put the Saints 2-0 up after Richard Keogh deflected in his early drive for the opener.
But the teams must meet again at St Mary's and Hasenhuttl was upset at his Premier League side's collapse.
"They felt too comfortable after 2-0 because it was a very good performance until that moment," he said.
"After the break the opposition tried to play more long balls because there was no way to go through our midfield pressing.
"For a long time we didn't give chances away and at 2-0 they were too sure they would win the game.
"It's a pity we didn't win, now we have another game and it's not something we want to have.
"We didn't want this game, we had a good chance to go through and we gave it away. We have to do it again with more concentration and more passion until the end."
Southampton looked on course for the fourth round when Keogh turned Redmond's low drive in after four minutes.
Redmond then curled in a brilliant 20-yard effort early in the second half to double the visitors' lead.
The England international has now scored four goals in seven games under Hasenhuttl after failing to previously net this season.
"He's coming back into good shape now and he's an important player for us," added the boss.
But Marriott started Derby's comeback when his smart half volley found the corner of the net after 58 minutes.
Lawrence's superb effort then complete the comeback three minutes later when he fired low across Angus Gunn from 25 yards.
Marriott still could have won it for the Sky Bet Championship side with the last kick of the game but blazed over from 16 yards.
Boss Frank Lampard, a four-time FA Cup winner, praised his side's mentality and welcomed a second chance.
"It wasn't so much the quality, more so the mentality, as that's what changed. There wasn't that much quality on the pitch but we were off it," he said.
"You can't come up against Premier League opposition and be like that. Our reaction was brilliant.
"It showed what we can do when we are at it. It's a lesson today, we got a draw but could have won.
"We beat Manchester United (in the Carabao Cup) and then went and lost at Bolton so the rules remain the same. You need to take the good things and you have to replicate them.
"I know they're not robots and it doesn't always go perfectly but we know we have got it in us. We need consistency.
"I would have taken it (a replay) at 2-0 down. With the squad we've got and the challenge to go to a Premier League team and play, it's great. We should embrace that."