The Saints defeated the Hammers 3-0 at the London Stadium after a first-half finish from Charlie Austin before Tadic added a second just after the hour-mark and then James Ward-Prowse wrapped it up in injury time.
"I think a really important three points for us," Tadic told the club's official website.
"The first half was really hard to play, we expected a reaction from West Ham because in the last couple of games they have conceded a lot of goals.
"We knew it would be tough in the first fifteen, twenty minutes. This is exactly what happened.
"After that when we scored a goal, I think it was much easier to play.
"We showed that we have a lot of qualities and that we can punish them."