He probably thinks he has a rough estimate of how old he is, but I've worked it out. I might not be 100 percent accurate, but he's MUCH older than he claims to be. Here's an example of the Doctor's age (and it's probably near enough):
The Doctor's Age (re-upload)
1st: The Doctor is born and lives for approximately 450 years before growing old and regenerating.
2nd: The Doctor lives as his second incarnation for around 200 years before being hunted down by his fellow Time Lords and forced to regenerate.
3rd: At the beginning of this incarnation, the Doctor is around 650 and regenerates from radiation poisoning at age 751.
4th: The Doctor apparently spends 65 years in this incarnation, as he regenerates at around 816 years old
5th: The Doctor lives as his fifth incarnation for around 87 years, and regenerates at the age of 903
6th: The Doctor lives as this incarnation for around 53 years before being attacked by the Rani, which causes him to regenerate.
7th: The Doctor spends around 600 years in this incarnation, before dying on the operating table after being shot down by a Chinese street gang in San Francisco. Luckily, though the regeneration process was delayed, he was able to repair his body and change his appearance once again. At this point, he's around 1556 years old.
8th: The Doctor spends a couple of centuries in this incarnation before getting trapped on planet Orbis for 600 years. After he recovers his memory and escapes, he spends a few centuries travelling and eventually gets involved in the Time War, which results in him ultimately regenerating into the War Doctor.
War: After regenerating from his 8th form at around 2656 years old, he fights in the Last Great Time War for about 800 years, and eventually regenerates into his 9th incarnation.
9th: Trying to put the terrible memory of the Time War behind him, the Doctor travels for around 100 years before meeting Rose. After travelling with her for months, the Doctor saves her life and regenerates.
10th: Upon regenerating from his 9th form, the Doctor is around 3556 years old. After a short lived six years in this form, the Doctor saves the life of Wilfred Mott after being warned of a prophecy that states "He will knock four times". Knowing that he's been running in vain, he puts his own self preservation aside and saves the old man. Dying of radiation poisoning, he eventually regenerates in his TARDIS, now around 3562 years old.
11th: About a day after saving Wilf and saying goodbye to his friends and companions, the Doctor's TARDIS lands in the front garden of Amelia Pond's house (who is around 7 at this point). Not long after leaving her behind to refuel the TARDIS, does he end up mistakenly travelling 12 years into her future instead of a few minutes. In the end, both Amy and her fiance Rory end up becoming the Doctor's surrogate family and companions. He leaves them to get on with their own lives for a while, and travels on his own for 100 years before eventually getting them involved in his escapades. Not long after this, do Amy and Rory eventually get warped back into the 1930s by a Weeping Angel during a trip to New York. Knowing he's lost them forever, he grieves and travels alone for around 100 years before meeting a Victorian version of Clara Oswald. After a short lived adventure with her, she dies. He spends a few hundred years trying to solve the mystery of the Impossible Girl before eventually meeting the current version of Clara (in the 21st century). He spends a year travelling with her until he ends up on Trenzalore, the planet where he was supposed to die. He ends up sending Clara back to her own time for her own safety, and spends 300 years protecting the people of Trenzalore from his enemies. Eventually, Clara comes back for the now 4363 year old Doctor, and tries to convince him to save himself, but he again sends Clara back to her own time, and stays for another 600 years. Tasha Lem uses the TARDIS to bring Clara back to Trenzalore, so the now decrepit and dying Doctor can spend his final day with his best friend. Clara succeeds in changing the future however, when she convinces the Time Lords to help save the Doctor from the Daleks. They agree, and give him a new regeneration cycle, resulting in the Doctor using the excess energy to utterly destroy them and their fleet. After the chaos, the Doctor is restored back to a youthful form, and regenerates into his 14th incarnation (as the Warrior and meta-crisis regenerations count) shortly after reassuring Clara that he will always be the same man no matter what.
12th: Currently, the Doctor is about 4963 years old.