Successive defeats to Barcelona and Sevilla have seen Madrid drop to third position, but after previously going on an 18-match unbeaten run to move to the top of the standings, Alonso is confident that Carlo Ancelotti's outfit can overturn the three-point deficit.
The 32-year-old told the club's official website: "The teams that beat us were on top of their games, we did not play well and made mistakes that we have paid dearly for.
"In La Liga, we have lost the lead we had, but you have to keep fighting because there could be surprises.
"Personal performances in those matches affected the team. It was not good news for us, but that's football, we were behind before and we came back."
Real Madrid travel to fifth-placed Real Sociedad on Saturday evening.