Neville felt his side could have easily gone in at half-time 3-0 down after they were overrun by a rampant Southampton display during the opening 45 minutes.
The Toffees moved to within three points of the Champions League spots in the Premier League courtesy of the draw but Neville was aware Everton were not at the races in the early stages of the game.
"We were so lucky to come in at half time 0-0," he told EvertonTV.
"If the score had been two or three nil to them I don't think we would have had too much to complain about.
"We just didn't start the game well. Southampton, with the new manager, came out of the traps really quickly. They had some chances and Tim Howard kept us in the game."
Everton were much sharper after the break and were guilty of missing some clearcut chances to take all three points with Neville, who turned 36 on the day of the game, left feeling the draw was a missed opportunity move even closer to fourth-placed Tottenham.
"In the second half, we played a lot better," he said. "We got control of the game and I thought that if there was going to be one team that would go on and win the game, it was us.
"We had some good chances - Victor [Anichebe], [Nikica] Jelavic and [Kevin] Mirallas all had good chances. But football's like that - no two halves are ever the same."