The Brewers were on course to cause a significant second qualifying round upset at Ings Lane, leading 1-0 as they did at half-time through Kieran Greenway's neat 20th-minute finish.
But, the Seals, who play their football three divisions above Albion in National League North, got back on terms early in the second period, then netted twice late on to seal a 3-1 success.
O'Connell, however, feels that things would have played out very differently had his side been able to add an all-important second goal.
"Overall, having watched it back and had the chance to take stock, I feel really proud of lads and really proud of the club for how everything went both on and off the pitch," he told the Harrogate Advertiser.
"The players will have slept well on Saturday night because they put in a massive shift, but we're still a bit disappointed by the manner in which we lost the game.
"Their first goal was a bad one to concede, and the second was a header - albeit a brilliant one from a great delivery - from a set-piece, and we pride ourselves on defending our box better than that.
"I don't think the score-line really reflects the game. Chester never broke us down or split us open. Some people will have watched it and say Chester had all the possession, but our game-plan was to give up the ball and not concede space.
"For me, we've gone toe-to-toe with a very good sixth-tier team, and we could have won it. If we execute a final ball better following a turnover we could have a second goal before half-time and at 1-1, Oli Norman goes clean through and should make it 2-1.
"Personally, I think we win the game if a second goal goes in, Chester were finding it hard work breaking us down and I don't see them recovering from that."
On the moment that saw Norman go one-on-one with Chester goalkeeper ? but fail to beat him after a loose pass across the visiting back-line was intercepted, O’Connell added: “We knew that there were areas where, if we could nick the ball, we could work a three-on-two, or get into an area to hurt them.
"That’s what happened for our goal, and we could have had another one before half-time if the pass is executed properly from a similar situation.
"But I think Oli Norman’s chance is the key moment in the game, if he scores that, Chester have a mountain to climb.
"I just think that he lost his composure a little bit because nine times out of 10 he scores that chance, he is usually very cool in those situations.
“Speaking to him afterwards, he didn’t realise how much time he had. If he goes low and across the keeper then I think he scores and we go on and win the game.”