Rayan Ait-Nouri canceled out Ibrahima Konate's opener for Liverpool before Mohamed Salah converted a penalty won by Diogo Jota for the 2-1 defeat.
O'Neil later said: "I think a fantastic performance and effort from the group who have had a tough week. We lost two starting centre-backs. One to a whole season and one to illness. Toti is back a week early with his hamstring and gets through the whole game. The lads gave everything and showed quality.
"They went toe-to-toe with one of the biggest clubs in the country. I am gutted for the lads with what they have given in the last six game they deserve more points for what they have given.
"Disappointing thing for me is one minute of losing control emotionally after we equalise and go chasing things took us away from the game-plan. That's the way it is going at the minute.
"Maybe at the end of the game we could be better with our decision-making. We are fighting some big clubs at the moment with one hand tied behind our back with some injuries - everybody knows the problems we have had at the club recently.
"There will always be individual errors in the game - Liverpool will have had loads. So it is always a collective.
"The responsibility of the result I accept that, but I also need to praise the lads for delivering performances against opposition like this.
"I know them well enough that they will feel disappointed for a day then they will be ready to go again."
On board having belief in him, O'Niel added: "I can't control other people's belief in me. All I can do is the best I can do."