Can I get into a good Management School like TAPMI, XIMB, XLRI, SPJIMR etc. after completing my B.Tech in 4.5 years due to one backlog?

Yes. Even though you have completed your B.Tech in 4.5 years due to a backlog, it is still possible to get into a good management school. But you have to put in a lot of hard work and dedication to achieve this. 

• First of all, you need to perform very well in your CAT/XAT exams and score at least 96 percentile. This will improve your chances of getting short-listed for GD & PI.
• For the Personal Interview round, you need to prepare very well. You must introduce yourself well to the people in the selection committee regarding your circumstances and try not to tell any fake excuses before them to get sympathy. They are very experienced in this field and have been doing it for years so they will definitely find out the truth. 
• If the committee thinks that you are a good scholar and due to some bad circumstances you are in this situation, then there will be no reason to disqualify you.

You might also be asked some difficult questions regarding your course and about your career, so also prepare for them very well and give your interview with full confidence. And if you are having some additional qualities like excellent in sports, extracurricular, leadership qualities, strong communication then your chances of getting selected will increase further.

Prepare well enough for your interview and try to present yourself as a perfect aspirant, avoiding any mistakes and you will definitely get selected at a top management school.