Lione Messi hit a hat-trick as Barca won 4-2.
"For me, [LaLiga] is the most difficult because in the Copa del Rey and other knockout competitions, one bad day puts you out," Valverde insisted.
"Here you have to have consistency."
His euphoria was clear to see on the touchline as the usually reserved figure went wild celebrating Lionel Messi's second and third goals to win the game.
"When you are chasing something all season, you say: finally!" Valverde remarked.
"In the end, LaLiga is very long, you have to go through autumn, a cruel winter, and we've been through it all.
"We have really wanted it since the beginning and we have done well to create a gap and I think we have been the best."
The moment was particularly special for the coach as it represents his first league title in his home country, having previously won the Greek Super League with Olympiacos.
"It's the first time that I have won it in Spain, I won three in Greece," he said.
"We're delighted, winning the league means being good a lot of the time and it would be unique to end the season unbeaten, extraordinary.
"For me, the double is difficult and hard to win... It's not too bad."