The experienced midfielder was angry with his side's poor performance after the break as they were held to a 1-1 draw by Valladolid
Sergio Ramos gifted Madrid a first-half lead, but Humberto Osorio's late equaliser saw Carlo Ancelotti's men drop two crucial points in the race for the Liga title.
Victory for Atletico Madrid this weekend will rule los Blancos out of the Primera Division race and Alonso did not disguise his anger at the way his side allowed Valladolid to snatch a draw.
"I'm annoyed with myself and with the team because we did not give the last 45 minutes the respect it deserved," Alonso told the official Madrid website.
"We were on top of the game despite the difficulties, because we knew if they scored it would be the equaliser. In the second half we lacked the intensity, focus and tempo demanded by the match. A lot was at stake for them and we were unable to maintain our tempo."
Madrid are now trailing leaders Atletico by four points with just two games to go, but Alonso refuses to give up just yet.
"It's not over, but it is now difficult. There is a small chance left but it is very unlikely. We have to do everything possible until the end.
"There are a lot of matches in La Liga and it's complicated. We haven't thrown it away but we've let points slip in certain matches and I don't think that would have happened if we were playing the football we are capable of."
Madrid meet Celta de Vigo and Espanyol in their last two league games of the season.