I got some minor damage(torn marks) to back side cover due to accidental spilling of glue stick. The last cover page got stick to its previous page. When I try to separate them it got torn a bit. Is this acceptable for travel or can I better go for a re-issue of passport ? Except this there is no other visual or physical damage.
To be safe, get a new passport.
After all you don’t want to arrive, and be refused entry when it could have been avoided.
As your passport is still recognisable you can apply for a replacement scheme:
In case your passport has not been damaged beyond recognition, i.e. passport number is legible, name is legible and photo is intact, then you can apply for re-issue of passport under the Tatkaal scheme. But, if passport has been damaged beyond recognition, then you cannot apply under the Tatkaal scheme. In that case, you need to visit Passport Officer at your nearest Passport Seva Kendra to get the passport on urgent basis.
More details can be found in this similar question.