The two teams at opposite ends of the table left the Emirates Stadium disappointed after claiming only a point from a chaotic clash which saw the Saints leading 2-1 at half time and 3-1 heading into the final two minutes of normal time.
Carlos Alcaraz capitalised on a mistake from Aaron Ramsdale to open the scoring for Southampton inside the first 27 seconds, before the January signing set up former Arsenal man Theo Walcott to double the visitors' lead after 14 minutes.
Gabriel Martinelli pulled one back for the Gunners midway through the first half, before the Saints restored their two-goal advantage on the 66-minute mark courtesy of a header at the back post from substitute Duje Caleta-Car.
However, Southampton were unable to hold on for three precious points and their first-ever Premier League win at the Emirates, as two late goals from Martin Odegaard and Bukayo Saka, the latter netting a 90th-minute equaliser, forced both sides to share the spoils for the second time this season.
While Arsenal's title hopes have been dealt another major blow, Southampton missed the chance to climb off the foot of the Premier League table and are now three points adrift of safety having played at least a game more than all of their relegation rivals above them.
Selles expressed his disappointment to have only come away with one point, but the Spaniard has taken plenty of positives from his side's performance in North London.
"We put a really good performance on the pitch. We wanted to take the three points - we showed it from the very beginning," Selles told the club's official website. "I'm a little bit disappointed because we didn't take the three, but very, very happy because of the character and the performance the boys put in today on the pitch.
"We always prepare the games to win the games. That's how we do it. We knew that to get something here today we needed to be brave and apply pressure high, and that's what we did in the very beginning.
"Sometimes it's difficult to keep that tempo and that pressing for 90 minutes, especially against Arsenal, who have a lot of players and a lot of solutions.
"We changed it at half time (replacing midfielder Alcaraz with defender Lyanco and switching to a back five), we stayed in the game, we managed to score the third one, and the game was a little bit long for us."
Explaining the decision to take Alcaraz off at half time after putting in an exceptional all-round first-half display, Selles said: "We had situations in the first half when they find their wingers very quick into the space, and we had Romain Perraud and Kyle Walker-Peters with yellow cards.
"We needed to make a decision - it wasn't an easy decision to take Carlos out of the game, but we needed to find five in the back to support the situations on the side two against one, and to have one more header in the defensive crosses.
"We made a small variation after two or three minutes of the second half because they changed the way they build up.
"The technical staff is doing a fantastic job. They support and see things very quick and they come with options we can use, and we can make good performances because of that."
Southampton have just six Premier League games remaining to climb to safety and will return to action with a home encounter against Bournemouth next Thursday.