The former Espanyol boss earned a point in his first game as Saints manager against the Toffees after the sacking of Nigel Adkins, and is ready to manage in an "amazing league"
Saints chairman Nicola Cortese controversially replaced Nigel Adkins with the Argentine coach on Friday after the axed boss guided the south coast club from League One to the Premier League in just two seasons.
But despite rumours of widespread planned protests from the home support, Pochettino was greeted with polite applause, and now says he is ready to start working to ensure his side survive in an "amazing league".
"I want to thank the supporters, they've been very kind with me and the reception has been amazing," he told Sky Sports via a translator. "I think tonight we've done very well and created seven good chances to score.
"I want to thank the players for the three days that they've been working with me, they've done very well.
"The only thing was that we didn't score any goals, we created a lot of chances and we were facing a very good side in Everton. They are fifth in the league so I think the team deserves a lot of credit.
"We did suffer a bit more in the second half but again we were creating chances and we just needed that bit of luck. We did very well today."
The 40-year-old former Espanyol boss also expressed his surprise at the scale of the atmosphere he encountered at St Mary's.
"I really enjoyed the game today," he added. "When you're watching it from outside you don't really realise how big it is, and just being in it you realise how amazing it is and why people who work here say it is such an amazing league."
Everton boss David Moyes rued his side's inability to take three points from the game as Victor Anichebe and Nikica Jelavic wasted glorious second-half opportunities after a slow start.
"I think after the way we played in the first half I was frustrated, but a little bit frustrated in the second half that we got one or two good opportunities and we didn't nick a goal," he told Sky Sports.
"From our first half performance we deserved to be down but I thought in the second half we deserved to win it and I thought we had one or two chances where we could have done it but we didn't quite get that goal."
And the Toffees boss feels credit must be given to Nigel Adkins for the side he has put together, despite the presence of a new manager.
He added: "I thought [Southampton] did really well and I've got to give Nigel a lot of credit because I saw his team play at Chelsea and they were excellent - I thought his players did the same tonight.
"Obviously there's a new manager in place now who takes over the reins and the team tonight did well - they're not a bad side, Southampton."