India lost the series-opener by 31 runs as the Indian batsmen, with the exception of Kohli, failed to tackle the English attack.
Opener Vijay (20, 6) and middle-order batsman Rahane (15, 2) contributed 43 runs together in their two innings at Edgbaston.
Ganguly, in his instagram post, wrote, "If you've to win a Test then everyone has to score runs."
He said, "This was the first Test in a 5 match series & I think this team has the capability to come back & play well. #AjinkyaRahane & #MuraliVijay will have to show some determination since they have scored runs in these conditions before.
"I don't think the captain is responsible for the loss. If you're the captain then you'll be criticised for a loss the same way as you're congratulated for a win."
The former India captain also warned against making wholesale changes in the wake of the defeat.
"One criticism for @Virat.Kohli is that he should give a consistent run to his batters & more time before dropping them. The failure against swing in English conditions can't be used as an excuse any more as everyone knows that it's what you get when you come to England.
"You can't be excused all the time & we have lost before in 2011 & 2014. You've to bat well. It's a very well known fact that the ball will swing in England the same way as Australia is known for its pacy wickets. So if previously you've scored runs there is no reason you can't now."
Kohli shone with his maiden century on English soil and followed that with a valiant fifty in the second innings.
"The captain should give confidence to his players. It's his team & only he can change their mindset. He will have to sit with them & tell them that if he can do it so can they. He should give them time & tell them to go out & play without any fear.
"It is true that after continuous chopping & changing of the playing XI, players can get afraid that after all these years they've failed to garner the faith of the team management."
Ganguly also said it was important for players to play all formats and cited the example of past Indian teams, which he said won overseas series because players stuck together.
"The good thing about the great teams of the past - whether it be #Australia, #SouthAfrica or our very own team which won the Test series here in 2007 - was that the boys used to play both formats of the game - #SachinTendulkar, #RahulDravid, #VirenderSehwag, including myself.
"So even if you played badly in 1 or 2 matches you got a lot of time to get back into form at the international level. Playing & scoring 150 in first-class cricket can't compensate for international cricket. In this team no batsman except Virat plays all the formats."
First Published: August 5, 2018, 6:07 PM IST