The Catalans beat Atletico Madrid 1-0 to ensure rivals Real Madrid cannot catch them at the top of La Liga.
Barcelona face Athletic Bilbao in the Copa del Rey final on May 30 before the Champions League final against Juventus on June 6.
“We have two more titles to win but we have picked up the one for consistency,” said Enrique, 45.
It means former Barca midfielder Enrique, who replaced Tata Martino last summer, has the chance to emulate Pep Guardiola by winning three major trophies in his first season.
Enrique experienced challenges off the pitch during his first few months in the role, facing criticism in January for leaving Lionel Messi and Neymar on the bench as Barca lost to Real Sociedad to leave Real Madrid in control of the title race.
“We started 10 months ago with many changes at the club which doesn’t understand the idea of transition and was coming off a season having not won anything,” said Enrique, who was also reported to have fallen out with star man Messi during training in January.
“There is no way that a trainer of a top club will not receive criticism during the year and I knew that.
“We knew that we wouldn’t be given time but we did our best.”
“The Champions League is more prestigious but this is more important. Last year we struggled a lot, we weren’t at the right level to be champions.
“You can’t win every year but there is no end to this cycle. We are a very young team – this is an historic day.
Real Madrid won 13 successive La Liga matches to lead the Spanish top-flight going into the winter break, but four defeats since the season restarted in January – plus two home draws against Villarreal and Valencia – have proved costly.
Their hopes of becoming the first side to retain the Champions League were also ended by last week’s semi-final defeat by Juventus.