India declared their second innings on 234-7 on Sunday, setting New Zealand a victory target of 284 at Kanpur's Green Park Stadium.
New Zealand's final batting pair of Rachin Ravindra and Ajaz Patel saw out the last 52 balls to force a draw in the first match of the two-Test series.
"I don't think so. That's not my reading of the game," Dravid, who took over the coaching role earlier this month, said when asked if India had delayed their declaration too long.
"Till half an hour before we declared, we were under pressure. All three results were possible, to be very honest with you."
India were 51-5 in the second innings before Shreyas Iyer stitched 50-plus partnerships with Ravichandran Ashwin and Wriddhiman Saha to prop up the innings.
Saha also added 67 runs with Axar Patel before India declared, leaving New Zealand to play the last four overs on Sunday.
"I thought we timed that declaration really well. We needed that partnership which was critical for us - from 167-7 to get to 234-7 was absolutely necessary," Dravid said of the Saha-Patel stand.
Setting New Zealand a smaller target could have backfired, the former India captain said.
"If they were chasing 240 to 250 in approximately 110 overs, then they're looking at 2.3 runs per over. That's not a lot of runs on the last day if a couple of batsmen get set.
"I thought we did it well, we timed it well. We managed to get a wicket yesterday and we came very close today."
The second and final Test is scheduled in Mumbai from Friday.