Matty Fryatt, making his debut in a one-month loan deal from Hull, gave the Owls a 43rd-minute lead against the run of play, before Seagulls midfielder Keith Andrews hit a last-minute equaliser.
Wednesday remain without a win in nine league outings this term but Jones, while disappointed to see two points snatched from their grasp right at the end, believes his men are now finally moving in the right direction.
He said: "I'm frustrated because one lapse in concentration in the whole 95 minutes has cost us. They weren't hurting us, they had become desperate, and if we'd kept our concentration that little bit longer we would have taken the points.
"I'm criticising them for one lapse. We should have dealt with the goal, because it was a simple long-throw. But I tend to be fair, and I think that on the balance of play and in terms of possession it was a fair result.
"We're getting better and moving in the right direction. In the last two games we should have taken six points. We just have too many players playing who need to get fit. Most of them are running on memory."
Jones hailed the impact of Fryatt and insists the 27-year-old striker could be the man, in the short-term at least, that helps to turn the Hillsborough club's season around.
He added: "His goal was a real striker's goal. He hasn't lashed at it, he's controlled it and passed it into the net. It's something we've been crying out for now for a really long time.
"He was running on memory at the end as well, though. Had he been that bit fitter we might have pushed on and with more care we would have gone 2-0 up.
"But we're not that far from where we want to be. We've been crying out for someone like Matty, and he'll play an important part for us."
Brighton boss Oscar Garcia refused to accept that his side were lucky to escape with a point after Andrews' last-minute leveller.
The Seagulls wasted a series of first-half chances but failed to seriously test Wednesday keeper Chris Kirkland after the break in their quest for an equaliser, until Andrews struck.
"When you have clear chances to score, you cannot say that we were lucky to get a point. They had one half-chance and scored," said Garcia.
"But we needed seven chances just to score one. Because they took their half-chance it made it difficult for us. You are chasing the game.
"It's important we have as many as players as possible that score goals, so I was pleased that Keith Andrews scored his first goal for Brighton."
Garcia admitted he was unsure how long striker Leo Ulloa will be sidelined for after he was stretchered off early in the second half.
He said: "It looks like a stress fracture. Tomorrow we will know for sure how long we will be without him, but we need him back as soon as possible.
"We have strikers injured, midfielders injured. He will be another on the list. It's important to have all your players to choose from.
"He's an important member of the team, so we will hope tomorrow for good news."