What an ignorant question that has been discussed to death SO many times here and on other sites. Here is the short answer:
1) the Mumbai police were simply overwhelmed by the scale of the attacks as they unfolded and the confusion that persisted at the time threw the Mumbai police into chaos. As the events unfolded there were literally 10,000s of reports and calls coming into the police control room of bombs all over the city and gunmen everywhere. The terrorists were smart enough to create such chaos by planting numerous IEDs in mobile targets such as taxis so the police were sent to numerous locations and the terrorists themselves optimised their numbers by splitting into small teams and constantly moving around.
The Mumbai police's plight was not helped by having the most senior members of its anti-terror squad killed by the terrorists in the line of duty.
2) the slow response by dedicated CT teams- NSG/MARCOs. Firstly the elite IN MARCOs who have a base in Mumbai were ready and waiting to be given the go to enter Mumbai but the Mumbai police/GOVT were initially reluctant to ask for outside help and/or realise the seriousness of the situation. Once the MARCOs were given the "go" they were on scene relatively quickly and able to contain the terrorists somewhat until NSG arrived. Secondly the NSG who are the country's dedicated CT force and whose role it was to combat such attacks faced serious delays in getting to Mumbai. The IAF IL-76 that flew them to Mumbai from Delhi where they are based had to be flown in from Chandigarh in Punjab. Once the NSG were on the ground they were effective in ending the situation but initial delays could not made up for.
3) the nature of this attack. This attack was the most audacious and revolutionary since 9/11- attackers coming in from sea and going on a murderous rampage in built up areas and hotels. Most police forces agreed their initial response to the attacks wouldn't have been any better. These terrorists had been trained by professional military of Pakistan and it was like a SF insertion rather than the typical rag-tag militia and their tactics and weapon handling mirror this. The fact the hotels/locations combined had over 4,000 rooms meant this was a MAMMOTH task for and SF and all SFs agree this was an incredible op by NSG which they couldn't have done any better in the same circumstances.
There are of course numerous other factors but I don't feel the need to go any more.
But I'm glad to report most if not all shortcomings realised during 26/11 have been resolved. NSG hubs have been raised in most major cities, most states/cities have raised/upgraded police QRT/SWAT teams to give adequate response as first responders including Mumbai/Mahrastra police who have QRT/ Force One. Also NSG have been given a MASSIVE upgrade that we can already see in recent vids and by 2014-5 they will be unstoppable. Also they have been given the means to commend ere any commercial aircraft in Delhi airport (where they are based) if a military AC is not available. (although during recent Mumbai blasts the NSG QRF were alerted and loaded onto a RAW ARC IL-76, based in Delhi, on the Tarmac and ready to respond within 15 mins). There are many other measures that have also been taken but, again, there's no need to go any deeper.
And the response to such scenarios is not measured in conventional military might. It is easy for you to sit there an question in hindsight but the fact this was a completely new form of terror sim
Ly can't be understated. NO ONE IN THE WORLD WAS READY IN 2008 FOR SUCH AN ATTACK.
. With "elite member" status comes cynicsm! 
