Croatian defender Lovren joined Southampton in the summer from Lyon and has been a key figure in the club's impressive start to the season.
Though a three-match losing run has dropped Southampton down to eighth in the Premier League, the club are still only five points adrift of fourth place.
Qualifying for the Champions League has been mooted as a long-term target for Southampton and Lovren was initially surprised to hear about those ambitions.
However, the centre-half believes Southampton need to dream of such a lofty goal and has praised the influence of Pochettino at St Mary's.
"'It will be difficult of course, but you know when you have a dream and you want it to come true, you can do it," Lovren told the Daily Mail. "We need to believe, everybody.
"When I joined the club, I was listening to the chairman and the manager explaining to me about the project.
"I was a little bit surprised and I didn't believe 100 per cent.
"But afterwards, when I saw pre-season and when they bought Victor Wanyama and Dani Osvaldo I was thinking; 'OK, now I see it's something serious and we can do it'.
"With Pochettino we have a top quality manager. We are all happy with this style of football, how we play now and I think a lot of teams respect us."