The Portuguese put Saints in front after just four minutes when he nodded in Adam Lallana's corner, but a Jos Hooiveld own-goal and 88th-minute Kieran Richardson strike looked to have snatched victory for the Londoners.
But Fonte was on hand to add his second on the 90-minute mark and secure a point, but the defender found it hard to revel in the glory of his brace come full-time.
"I'm obviously very happy with [the goals], but I've got mixed emotions because we failed to keep a clean sheet," he told Saints Player
"I'm a defender and every defender would be disappointed with that, although I know it's not only the defenders who are to blame.
"As a team we have to defend better by stopping these mistakes because conceding goals is costing us points.
"This wasn't the only game – there have been other games where we've been comfortable and then there's been a period where we just concede goals.
"It has to stop so we'll work very hard on the training ground to do that. We must make sure we concentrate for 90 minutes – not 60, 70 or 80.
"The goals meant a lot because we have been in this situation – where we were winning then we conceded goals – before," continued Fonte.
"It felt very emotional because it meant we got something from the game, so I was pleased for the team."