Valencia, sporting a host of new faces, had few ideas going forward but levelled when Jonas headed in from a free kick.
"I expected more from my team," Mourinho said. "We haven't played a great game, but we did enough to win."
Later, rivals Barcelona began their campaign with a 5-1 routing of Real Sociedad.
The visitors were three goals up in 31 minutes before last season's Europa League and Copa del Rey finalists responded in the second half.
Bilbao's Oscar De Marcos got a goal back just after the break and Mikel San Jose then struck twice to level the scores with 14 minutes to go before Betis finally triumphed late on through Alejandro Pozuelo and Jorge Molina with his second.
In the day's other game, Levante drew 1-1 at home to Atletico Madrid.