Messi's hat-trick at Deportivo La Coruna gave Barcelona a 4-2 victory and an unassailable 11-point lead over second-placed Atletico Madrid.
In its first season under manager Ernesto Valverde, Barcelona has reclaimed the league title from nemesis Real Madrid and sealed a third championship in the last four campaigns.
The lone domestic blemish was losing to city-rival Espanyol 1-0 in the Kings Cup in January, although Barcelona turned around that first-leg deficit and thrashed Sevilla 5-0 in the final on April 21.
Barcelona is now just four games away from becoming the first side to go unbeaten through an entire season in Spain's top division.
Next Sunday it faces a huge test against Real but Messi said he and his teammates should take the time to "celebrate" the achievement.
"We feel so much joy after winning this league," the Argentine told Barcelona's TV channel. "We know how complicated it is to win the league, which is why we have to cherish this and celebrate it as we should with all our fans.
"We were superior to all our rivals and we haven't lost a single game. We only lost once in the Cup and in Roma where we had a very unexpected result," Messi added, referring to the 3-0 Champions League second-leg defeat that saw Barcelona exit the quarterfinals on the away goals rule.
"You always deserve a lot of credit when you win a league, and to do so without losing a game is very difficult.
"We had some tough moments and we overcame them without losing and that's incredible."
Valverde was criticized following the Roma result but Barceona left-back Jordi Alba sprung to his defense Sunday. The Spanish manager has brought a more balanced approach to Barcelona since replacing Luis Enrique last year.
"He has managed the dressing room perfectly," Alba told reporters. "The Roma defeat annoyed us a lot but we've had a very good season.
"We have won the double. Roma was a difficult moment, but it should not erase what we have achieved in the last week."
There may be difficult moments to come when playing Real, despite Los Blancos having an off-season in the league.
No extra motivation will be required for Zinedine Zidane's squad given the rivalry and Real will be in buoyant mood if they finish off -- as expected -- a depleted Bayern Munich in the second leg of their Champions League semifinal Tuesday.
Real -- European champions in each of the past two seasons -- won the first leg 2-1 in Munich.
But with Messi in form, Barcelona certainly won't be overawed.
With his hat-trick, he moved one goal clear of Liverpool's Mo Salah in the race for the European Golden Shoe on 32 goals.
And while Messi has four games remaining, Salah has only two left in the English Premier League.