"Today we showed the same consistency we have been showing. If people saw in the game that we were lazy or arrogant or trying not to win the game -- it was completely the opposite," Guardiola said.
For the first time since they were beaten 2-0 by Palace on October 30, City finished a league game without all three points.
They remain firmly in pole position for a fourth title in five seasons, but their draw on the south coast will give a glimmer of hope to Liverpool and third-placed Chelsea.
Guardiola is unconcerned by the possibility of Liverpool closing the gap.
"I feel as a manager confident for the future with the way we are behaving. Without the ball, everybody helps each other. I know how difficult this stadium is, with the way they play and how good we have played," Guardiola said.
"I don't understand the way people say that now, after this result, the race is open, when before it is over. But this is your job to talk about that. I would love to be 40 points ahead of Liverpool and Chelsea, but that's impossible. I would never expect to be in this position, with this margin."
City were rocked in the seventh minute when Walker-Peters linked up with Nathan Redmond on the right flank.
Walker-Peters cut inside and, with City backing off, the right-back had space to shoot into the far corner with the outside of his foot.
Frustrated by Southampton's high-energy display, City were struggling to find their usual rhythm.
Laporte saves City
Raheem Sterling nearly snatched an equaliser against the run of play with curler that whisted just wide from a tight angle.
Sterling should have brought City level moments later, but the forward fluffed his lines from Phil Foden's pass, allowing Fraser Forster to save his under-hit close-range effort.
Ederson made an instinctive stop to keep out Jan Bednarek's near-post header early in the second half.
Rodri's miscued strike from the edge of the area almost caught out Forster, who turned it around the post at full stretch.
Laporte made a superb last-ditch block to frustrate Armando Broja after the Southampton forward raced clean through on goal.
Broja should have scored from the resulting corner, but headed James Ward-Prowse's delivery against the woodwork from just four yards.
It was a crucial miss and City finally equalised in the 65th minute as Laporte exploited Southampton's weakness in the air.
Kevin De Bruyne swung a free-kick to the far post and Laporte was left completely unmarked to score the 11th headed goal against Southampton in the league this season.
As City pushed for a winner, De Bruyne hammered a 25-yard rocket against the post and Forster saved Gabriel Jesus's header with his legs.
City were denied a penalty after VAR ruled Oriol Romeu's foul on De Bruyne had taken place just outside the area.
Stuart Armstrong was fortunate to escape a red card following a VAR check of his high foul on Laporte.
In the tense final minutes, Forster pushed away Foden's goalbound deflected cross and De Bruyne's close-range effort was repelled by the inspired Saints keeper.