The Irishman has claimed that the Lions could have secured a historic victory had they been coached more effectively.
"If we had a little more structure during the weeks, and more of an attack gameplan, driven way earlier in the tour, I think we could have won 3-0," BBC Sport quotes O'Brien as saying.
"With the players we had, we should have won the series."
Lions chief executive John Feehan has responded to O'Brien's remarks, insisting that the "best coaching team available" was in place and praising the Lions' performances against New Zealand.
"People will always have their views on what could have been done better but the fact is that, against all the odds and with limited preparation time, this squad became only the second Lions team in history to either win or draw a series in New Zealand in 13 attempts," he said.
"That achievement cannot be underestimated."
The 1-1 draw marks only the second stalemate between the two teams in history.