The tourists trail 3-1 in the seven-match series, making Sunday's fifth game at Headingley a must-win if they are to keep their hopes alive.
"We have played some of our best cricket when we've had our backs to the wall," said Dravid.
"We have spoken about that but it is a case of going out and executing it.
"We know we have our backs to the wall here but the boys are also aware that the games were close.
"If a few things went this way or that way the scoreline could be very different. So that is at the back of our mind."
India looked set to level the series 2-2 at Old Trafford on Thursday when they had England struggling at 114-7 in pursuit of 213.
But an unbroken eighth-wicket stand of 99 between Ravinder Bopara and Stuart Broad took England to victory.
"It was disappointing but I haven't felt it has damaged morale as such," added Dravid.
"We have discussed the fact we maybe need to maintain the energy levels right through until the end of the innings.
"Maybe towards the last 25-30 runs those levels did dip, the boys had really tried hard and maybe the disappointment crept in, but we need to keep fighting right until the end."
India have fitness concerns over Sourav Ganguly and Zaheer Khan for Headingley.
Left-arm paceman Zaheer has a swollen ankle, while batsman Ganguly missed practice on Saturday due to illness but is expected to play.
"If his (Zaheer) ankle is fine and holds up then great," said Dravid. "It was a bit swollen after the last game but it has come down drastically in the last 24 hours.
"We obviously want our best players in a game like this, when you know you have to win the next couple just to stay alive in the series.
"But if he is not fit he is not fit, we will play someone else."
Should Zaheer be ruled out, Munaf Patel is his likely replacement in the starting XI.