MADRID, March 6 (Xinhua) -- Tuesday has to go down as one of the worst days in the history of Real Madrid, after a humiliating 4-1 home defeat to Ajax saw them crash out of the Champions League at the last 16 stage.

The defeat is painful enough in itself, but is made worse by the fact that it came off the back of two home defeats to FC Barcelona within four days of each other. Those defeats not only ended Madrid's dreams of reaching the final of the Copa del Rey, but also leaves them 12 points behind Barca in the race for the La Liga title with just 12 games left to play.

Real Madrid are effectively out of the race for all three of this season's major titles with two and a half months still to go in the season.

Even before Tuesday's defeat, the future of coach Santiago Solari was up in the air, with the media debating not whether Madrid's former B-team coach would keep his job, but instead who would be his replacement.

Solari may survive until the end of the season, if only because there seems little point in bringing in someone else for the remaining few matches, but he is clearly a dead man walking and Madrid will have a new coach in the summer.

The coach won't be the only one to pay for what right back Dani Carvajal called a "s**t season" when he spoke to the press on Tuesday night, with several big-name players also likely to be on their way.

The club will look to shift Gareth Bale, who has come in for huge amounts of criticism from the press over his performances, his injury record and his attitude. Some of the criticism is harsh for the man whose goal led Madrid to last season's Champions League title, but if the press are being allowed such a free reign to attack Bale then it is because nobody at the club has objected, and that means Madrid want to sell.

Left-back Marcelo is also likely to leave after his defensive flaws have been exposed too often this campaign. Toni Kroos also looks as if he has had enough, with the midfield general also running out of fuel this campaign, while Isco's conflict with Solari will also mean he is probably shown the door, even if there is a new man in charge.

As for Karim Benzema, he briefly flickered at the start of the year and began scoring goals on a regular basis, but those goals have dried up along with Real Madrid's results.

Solari does deserve credit for some of the good news for Real Madrid this season, with the development of left-back Sergio Reguilon, the explosion of Vinicius Jr and a series of solid displays from Marcos Llorente, whose progress has been halted by two groin injuries.

Indeed, a fit Llorente would certainly have done a better job than Casemiro did in midfield on Tuesday.

However, neither coach nor players should shoulder all of the blame, and it should be remembered that last season saw Real Madrid finish third in La Liga, 17 points behind winners Barcelona, and that they were knocked out of the Copa del Rey by Leganes.

Winning the Champions League was a great achievement, but it also papered over the cracks in the squad and led to overconfidence.

The league and cup displays showed that the Madrid squad needed work, but instead of strengthening over the summer, club president Florentino Perez sold Cristiano Ronaldo to Juventus, losing a striker who had scored 26 league goals and 15 in the Champions League that year.

Zinedine Zidane probably knew what was coming when he stepped down as coach just days after that Champions League win.

Julen Lopetegui's arrival was surrounded in controversy as he was sacked from the Spain squad for his decision to join Madrid weeks after penning a new deal as national team coach, and it probably didn't help that the former Madrid goalkeeper hadn't been first choice to replace Zidane.

The club re-signed Mariano Diaz as a late replacement for Ronaldo, but the striker has struggled with injuries all season and wasn't even in Tuesday's matchday squad.

Neither was right-back Alvaro Odriozola, signed for 40 million euros from Real Sociedad when Madrid already had Spain international Carvajal in that role.

The only summer signing in Tuesday's team was goalkeeper Thibaut Courtois, another player many would argue was only signed because he was available at a knockdown price and who has not been an improvement on previous incumbent Keylor Navas.

So after his team finished 17 points behind Barcelona last season, Perez did nothing to strengthen the Real Madrid squad. Is it really a surprise this season has been worse than last?

To many, it seems obvious the club needs some new blood in the first team and that some veterans may have to go. Solari's reputation has been so damaged by the events of the past week that he cannot possibly continue as first-team coach beyond this season, but anyone looking for the root of Real Madrid's problems would also do well to cast their gaze at the directors' box.