The BBC pundit heaped praise on Spurs' young team.
Indeed, the former Arsenal defender heaped praise on Mauricio Pochettino's men for showing 'a bit of character' at St Mary's.
The north London side were up against Pochettino's former club and trailed the Saints twice. But Erik Lamela hit back for Tottenham first, while Nacer Chadli grabbed Spurs' equaliser after Southampton had scored their second.
And Keown feels it is a good sign for the future - with Pochettino possessing a good 'core' at White Hart Lane, in his view.
The BBC pundit said on Match of the Day: “A lot of people are saying that Tim Sherwood should have stayed in the job.
“But I’m a believer that he (Pochettino) has got a nice core there. You’ve got [Ryan] Mason, [Eric] Dier and Harry Kane. It’s a very young team.
“And they showed a bit of character today, which is something that they haven’t done recently."
The former Arsenal man did, however, raise a note of caution in response to Gary Lineker mentioning that Spurs are currently worse off than they were at this point last season.
Keown added: "But there has been a lack of progress and, with the stadium developing, you wonder where the success is going to come from.”
Tottenham remain above Southampton (by a point) after the 2-2 draw and sit sixth in the Premier League. Liverpool only lead the north London club on goal difference but do have a game in hand.
Spurs' chances of a top-four finish, meanwhile, realistically look over. Fourth-placed Manchester United are seven points clear - also with a game in hand (which will be played against Everton later today).