The Barcelona star scored both of Barcelona's goals in a 2-1 win at Real Betis to beat the 40-year-old record.
"The record is great for what it means, but the most important thing is that the team won and that we maintained the distance with the teams behind us," Messi told the club's website.
"When the year starts the objective is to win it all with the team, personal records are secondary."
But he added: "I'll try to score more goals to make it more difficult for the next player that tries to break it."
The 25 year-old drew level with Muller's mark after 16 minutes with a trademark diagonal run and left-foot finish. It took him just nine more minutes to take the record as his own.
This time he profited from one of his chief assist-makers, Andres Iniesta, whose clever backheel found Messi in the merest of space only he needs to find the net with his left foot.
Messi almost marked the occasion with a hat-trick late on but his shot from close range was parried onto the post by Betis goalkeeper Adrian, with Jordi Alba crashing the rebound off the crossbar and over.
Barca coach Tito Vilanova said on his team's website: "We're pleased that Messi helped us out with his two goals and that he broke Muller's record.
"He still has three matches left this year, let's see if he can extend his record. We hope that he still has a lot left to give because he's still very young. He's a world-renowned star that has a series of attributes that make him nearly unrepeatable."
But the coach would not get drawn into speculating how many goals he might go on to score.
"We shouldn't heap more pressure on him," said Vilanova.
"His record this year is absolutely brutal. Let's enjoy the moment and not focus on how many goals he might score in the future."
The Argentina international's goals also sent him clear of Cesar Rodriguez as Barcelona's all-time leading league goalscorer after they had been level on 192 before the match.
Messi has scored 56 of his 86 goals in the Primera Division. He has also score 12 times for his national team including a stunning hat-trick in a 4-3 win over Brazil in June.
His remarkable feat has unsurprisingly made Messi the favourite to be crowned world footballer of the year for a fourth successive year.
He was last month named on a three-man shortlist for the Ballon d'Or alongside team-mate Iniesta and Cristiano Ronaldo.
"If Iniesta wins it will be fully deserved and I would be delighted," Messi said.
"It's a title for the whole team."
The winner is due to be announced on January 7.