Real's championship challenge has suffered two setbacks in the space of a few days, after they went down 4-3 against Barcelona in Sunday's El Clasico before a 2-1 defeat against Sevilla on Wednesday.
That leaves them third in the table - two points off Barca and three away from leaders Atletico.
And if Real are to clinch the title, Alonso says that they cannot afford anymore slip-ups.
"The margin of error is minimal. We must win all our remaining games," he said.
"We wanted to forget (the Barcelona defeat) and come here (to Sevilla) and win but sometimes we haven't been on at our best level.
"Our last two games have been negatives and little else. We have had many chances but it wasn’t to be. We still have to believe."
Real can bounce back on Saturday at the Bernabeu when they face Rayo Vallecano.
