After the match, Pochettino was asked about his thoughts regarding England's top flight competition and he responded positively.
"I really enjoyed the game today," he told Sky Sports 1.
"When you're watching it from outside you don't realise the dimensions and how big it is, but when you're inside you realise how amazing it is and why people who have worked here say it's such an amazing league."
And Pochettino also commended his Southampton players and the clubs supporters for helping him through his first game.
"I want to thank the players for the three days working with them, they have done very well," he said.
"I want to thank the supporters for the very kind reception they have given me, it was amazing.
"Tonight we have done very well and created at least seven good chances to score.
"The only shame was that we didn't score the goals but we created a lot of chances facing a very good side in Everton who are fifth in the league. We deserve a lot of credit although we did suffer a bit more in the second half.
"But we were creating chances and just needed that bit more luck."