The 104-ranked India are ranked 83 places above Bangladesh in the FIFA rankings.
After holding Asian champions Qatar to a 0-0 draw last month, Sunil Chhetri and Co. will be eyeing to notch their first win in group E to keep their slender qualification hopes alive.
"The pressure is actually on India because they're going to be playing in front of a big packed house. If India lose, it's a big upset, so we are aware that they'll be under a lot of pressure," the 55-year-old told reporters ahead of their game.
"It's a big motivation when you come to play in Kolkata knowing that it's going to be a full house playing against India at the Saltlake Stadium."
The coach lauded Bangladesh's show against Qatar as they lost 0-2 in Dhaka in their last qualifier game, but created a flurry of chances.
"We all know how bravely we played against Qatar and we can cause India a problem. I think the pressure will be on India and not so much on us. We are hoping to maintain the same level of intensity as we showed against Qatar. If we can put up a good performance, the result will look after itself," he added.
India will be missing the services of star defender Sandesh Jhingan and Anwar Ali (Junior) but Mimms said the Sunil Chhetri-captained side are still a force to reckon with.
"We're not taking India lightly despite the fact that they have got a couple of injuries. They have got other good players who play at a good level in India. No matter what 11 they put out it's going to be a good team," he expressed.
Quizzed how he's prepared his team's goalkeepers to deny the goal-poaching ability of Sunil Chhetri, he said: "We've just got to stick to our gameplan and work at it and hopefully it nullifies any threats."
"Obviously Chhetri scores a lot of goals and he's a good player in the ISL and for the India team he is a talisman. We've got to be aware of him an also there are 10 other on the pitch. We've got to be aware of the things and tactically and technically we've prepared our goalkeepers," he added.
( With inputs from IANS )