An early header from diminutive Emanuele Giaccherini at St Mary's looked set to secure the Black Cats' first win of the season.
However, Jose Fonte's last-gasp header secured Saints a deserved 1-1 draw and strengthened Di Canio's resolve when it comes to improving his squad further.
"When I asked 45 days ago for another central midfield player with a physical presence, with good quality and ability, preferably British, there was a reason," the Italian said.
"I know this league better than some managers who have managed for 20 years in England. I know, this is why I continually asked for two more players with a physical presence.
"I had the same situation two years ago at Swindon, a different level. We brought 12, 13 players from abroad and straight away I said I wanted two, three British ones with a physical presence.
"At the end of the season we won the league. Obviously I can't promise we'll win the league here but it is obvious that we will have less problems."
Di Canio did not enjoy the best preparation for the match, having been involved in a late-night altercation with drunk Southampton fans.
His side looked unaffected, though, and he was proud of the way in which they dealt with Saints' attack
"I feel 50-50," Di Canio said. "Obviously we defended for the whole game, like Fulham did against us last week.
"The defence have done an amazing job because playing Lambert, Rodriguez, Lallana and then Ramirez and Osvaldo - I tell you, this is one of the best sides up front in the league.
"Their frontline gives them a chance for them to finish in the top 10, play good football, a physical presence, energy and quality.
"My back four, central midfield and wingers, have done a very, very good job in defensive moments."
Sunderland's resilience was impressive, but Southampton's leveller was deserved.
Fonte's goal had been coming and continued their unbeaten start, although manager Mauricio Pochettino was left frustrated at what could have been.
"At the moment, I am not really happy," he said. "I am more disappointed
"I am not disappointed in the way we conceded the goal early on - I take full responsibility for that.
"That is not acceptable and it will serve as a wake-up call because it can never happen ever again. It is not right.
"At the same time I am happy and content with our industry during the second half.
"We created a host of chances and, if you look at the second half, we deserved to win the match.
"We secured a draw in the last few minutes of the game and it showed us that all the work we did after conceding that early goal was important and we fully deserved to get that goal. Perhaps even more.
"I am very clear that in the sense that we've had a very good pre-season. It shows in the effort that we put in today, that we are physically strong over 90 minutes like we were last week as well."