Gavaskar also wished that India have no bad days in knockouts.
The 2023 edition of Asia Cup is slated to get underway on Wednesday (August 30) with the Pakistan versus Nepal encounter in Multan.
The Men in Blue will open their campaign against arch-rivals Pakistan in Pallekele on Saturday (September 2).
This continental tournament will be a big part of India's preparations for the ODI World Cup, starting on October 5 in Ahmedabad.
"I don't think there's any other cricket team in the world which is under as much pressure of expectations than the Indian team," Gavaskar said in Mumbai at the release of veteran cricket administrator Amrit Mathur's book 'Pitchside: My Life in Indian Cricket'.
"Because every match that the team plays, the fans, the followers - not just in India, but across the world - expect and want India to win," he added.
"In sport, we all know that sometimes you win, sometimes you don't. The pressure can be telling and I think that's the kind of pressure the Indian team is currently experiencing with everyone wanting them to win the Asia Cup and the World Cup - which will be held in a month and a bit," he further said.
Gavaskar urged the fans to be more “understanding” of the pressure situations and also expressed his wish that the Rohit Sharma-led side manages to avoid any unfavourable outcomes during the knockout matches.
"This is where, we, as cricket followers, need to show a bit more understanding," Gavaskar stated.
"There will be days when the team will not be able to play up to its potential and let us keep our fingers crossed that if these days come, they happen at the league stage and not at the knockout stage," he remarked.
Gavaskar believes "cumulative prayers" can work well for athletes, like it did in case of Neeraj Chopra a few nights ago, when he became the first Indian ever to win a gold medal at World Athletics Championships.
"With cumulative prayers from all of us, we will be able to pray for India to win not only the World Cup, but also the Asia Cup," Gavaskar said.
"As a nation that follows sport, we prayed for Neeraj Chopra to win. We stayed up to be able to watch, we had hearts in our mouth, hoping and praying that he would win and he did.
"This is what I request all of you, to convey to other Indian sports lovers to please do that so that our team goes on to win both the Asia Cup as well as the World Cup," he added.
(With PTI Inputs)