O'Neill, who thought his side would end their 11-year win-less run against Everton, was frustrated with the result.
"We should have been out of sight at half-time. Instead of being one up we should have been three up," he said
"Having said that, the players played brilliantly away from home against a side who have a great chance of being in the Champions League.
"It was a great performance by the players. To be fair I thought we were exhilarating in the first half.
"We knew we would be under pressure in the second half but I always thought on the break we looked dangerous.
"The second goal epitomised a bit of luck and a bit of misfortune.
"We are obviously very disappointed."