Spurs have qualified for the Champions League in each of the past three seasons despite operating with a significantly smaller budget than many of their direct Premier League rivals, but they have not won any silverware since lifting the League Cup in 2008.
Speculation has begun to grow over the future of Pochettino following another trophyless campaign, but Eriksen believes that they are ready to make the next step forward.
"We've been very stable. People should look at the stabilisation of the team and our achievements in the Premier League," the Denmark international told the Evening Standard.
"The next step is, of course, to finish the semis and try to get through [to a final]. I think if we do what we did against all the teams in the Champions League again, we have a chance of going even further.
"I think we've shown in the Champions League we have something we can take with us. We're over the hill, we tried it. Now we want to win something, we want to go further. Mentally that's a big step we need to go forward."
Spurs reached the semi-finals of the FA Cup this season, only to lose to Manchester United at Wembley.