KKR scored just 84/8 in their allotted 20 overs after winning the toss and opting to bat first in Abu Dhabi.
McCullum said KKR were quite "timid" in their response to some quality RCB bowling in the first half, where they managed a score of only 84/8 in their 20 overs, with no one barring skipper Eoin Morgan (30) looking in any sort of rhythm after a top-order collapse.
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Tailenders, Kuldeep Yadav (12) and Lockie Ferguson (19*), were the only others to move past the 10-run mark in one of KKR's worst batting performance in IPL history.
Having stressed to his wards the need to show positivity on the field, McCullum was left head-scratching over their lack of intent on the night.
"Before the game we spoke about showing some intent especially at the top of the order and, unfortunately, we lacked that tonight," he said at the post-match press conference, as quoted by Cricbuzz. "So that's something we have to address. We were very poor with bat in hand. You are not going to win too many games from 40 for 6."
"We are still fourth in the tournament, which is very fortunate for us. The destiny is still in our hands. We have to tidy up some of the areas. It's just that we were very timid in our approach."
"That's a bit frustrating because we spoke at length before the game about trying to be positive and show some strong intent. If you are defending 84, you win one out of 150 games. Tonight wasn't good enough from the batting point of view," he added.
McCullum, though, also acknowledged the efforts of RCB's Mohammed Siraj (3/8), whose new-ball burst combined with some incisive bowling from the rest, didn't let the KKR batsmen breathe comfortably at the crease, a performance their own bowlers couldn't replicate.
"RCB bowled really well. Siraj bowled excellent lines and lengths. He was able to present the seam and ask a few questions to our batsmen. Questions which, in the past, we would have answered better than what we did tonight," he said.
"We have to bounce back because we have a game in a few days time. That will be the nature of the tournament as well with the conditions being challenging. We have to find a way to pick ourselves and find results when it's challenging."
"We had planned that they will hit us with their seamers. Here in Abu Dhabi, it's been quite useful for the seamers. If you flip it, [Aaron] Finch was trying to walk at the bowlers and trying to ask some questions."
"Sometimes that's what you have to do. You have to be creative to get yourself into the game. We have to find a way to enter the game and you can't be in a situation that we were and expect to win. I don't think we were able to enter the game at any stage. None of our top-order batsmen were able to get going," the coach added.
After their fifth defeat in ten outings, KKR next face Delhi Capitals (DC) on Saturday (October 24).