Alvarez has been criticised by Sevilla fans since their shock failure to qualify for the group stages of the Champions League last month, and they chanted for him to go after a 1-1 draw at home to Racing Santander during the week.
"There aren't so many problems, it's our first league defeat but we must remain calm," he told the club's radio station after a rare start this season.
"It's not a good moment but it isn't a crisis. We aren't playing as we have done, but we have the players to turn this round."
Alvarez has never quite won over fans since replacing Manolo Jimenez in March, even though he led them to victory in May's King's Cup final.
One of the bones of contention with fans has been his apparent unwillingness to use Fabiano, Brazil's leading striker from the World Cup finals.
"He's a good coach it's just that in football you have good and bad moments," he added. "He is capable of getting through this, is calm, knows what he wants, and is working well.
"After our Champions League exit there hasn't been much patience shown towards us but we are working hard.
"I haven't had the minutes I expected this season. It's strange because it isn't something I expected after extending my contract but I have to have respect for my colleagues and coach and prove that I am the important player I want to be."
Alvarez has a tough week ahead of him to put things right starting with a Europa League trip to play Borussia Dortmund followed by the visit of Atletico Madrid in La Liga next weekend.
