Putin’s speech does mention India:

We welcome today all our foreign guests while expressing a particular gratitude to the representatives of the countries that fought against Nazism and Japanese militarism.
Besides the Russian servicemen, parade units of ten other states will march through the Red Square as well. These include soldiers from Armenia, Azerbaijan, Belarus, Kazakhstan, Kyrgyzstan
and Tajikistan. Their forefathers fought shoulder to shoulder both at the front and in the rear.
These also include servicemen from China, which, just like the Soviet Union, lost many millions of people in this war. China was also the main front in the fight against militarism in Asia.
Indian soldiers fought courageously against the Nazis as well. Serbian troops also offered strong and relentless resistance to the fascists. Throughout the war our country received strong support from Mongolia.

We are aware that US veterans who wanted to come to the parade in Moscow were actually forbidden to do so. But I want them to know: We are proud of your deeds and your contribution to our common Victory. We honour all soldiers of the allied armies – the Americans, the English, the French, Resistance fighters, brave soldiers and partisans in China – all those who defeated Nazism and militarism.