Antoine Griezmann’s late strike means the Spanish side will take a valuable away goal back to the Wanda Metropolitano for next Thursday’s second leg.
It was an outcome that looked unlikely when Sime Vrsaljko was dismissed for collecting two bookings inside the opening 10 minutes at the Emirates Stadium.
Simeone was sent to the stands by referee Clement Turpin for his protestations, but watched his side produce a backs-to-the-wall performance to earn a 1-1 draw, with Jan Oblak particularly impressive in goal.
The Argentine manager afterwards cited their Champions League semi-final against Barcelona in 2016, when Fernando Torres was sent off in the first leg at the Nou Camp but they still progressed to the final.
He also mentioned a La Liga fixture, also against Barcelona, from earlier in 2016 when Filipe Luis was sent off early in the contest, but Atletico went on to lose 2-1.
Simeone said: ‘Surviving in the Europa League would be the best way to describe it.
‘I remember a game in Barcelona when Filipe was sent off after 13 minutes, or another Champions League game when Torres was sent off.
‘The team has done fantastic work for a number of years. In a stadium like this, the attacking football Arsenal played, the team had to keep going every minute. That’s the most beautiful thing about football.
‘It’s really hard to play away at Arsenal – an extraordinary stadium, a spectacular coach in the opposite dugout – with 10 men.
‘These Atletico players, the way they played and put up with the pressure was tremendous. The fans brought a positive energy to accompany our passion.
‘You guys have no idea how difficult it is to defend. Football is about playing and playing is the fun part, but you’ve got to have balls to defend with 10 men for 80 minutes.
‘If you play normally you have more possibility [of scoring], but defending like that shows real character – it’s a message for those who come along with us.’