Saints secured their sixth straight title and 11th overall with a 4-0 win over Bangor City.
They will play in next season's Champions League qualifiers and Harrison wants to emulate Irish side Dundalk.
"Dundalk showed every club of our size the way by getting into the group stages of the Europa League," he said.
"That's certainly our goal and where we want to be."
League of Ireland's Dundalk featured in this season's Europa League group stages having come within one round of reaching the Champions League.
Saints have not progressed beyond the second qualifying round of the Champions League during Harrison's six years in charge and they lost to Apoel Nicosia in July.
Harrison said next season's Champions League campaign would be the motivation for his players in their remaining seven league games of the season.
"They want to be putting themselves in the team and the squad for Europe," Harrison told BBC Wales Sport.
"It doesn't stop. It's a continuous cycle and wanting to play in European football."
Saints' only defeat in the league was away to Carmarthen Town in February but Harrison said the campaign had not been easy despite his side's dominance.
"I think we've been very, very good," said the former Middlesbrough and Crystal Palace player.
"We've been fresh, we've had new zest, impetus and young players that are hungry."
Harrison's side remain on course for a third successive Welsh domestic treble.
Having already won the league and the Nathaniel MG League Cup, Saints face Gap Connah's Quay in the Welsh Cup semi finals on 1 April.
In December the Oswestry-based club broke a 44-year-old world record held by Dutch giants Ajax for the longest winning streak in top-flight football.
Saints also reached the semi-finals of the Irn-Bru Scottish Challenge Cup, securing away victories over Forfar Athletic and Livingston before losing to St Mirren.
"The Irn-Bru Cup was fantastic as well and we're very disappointed we got knocked out there but we gave a good account of ourselves and Welsh football," Harrison added.
New Saints boss Craig Harrison has targeted progression in Europe after winning the Welsh Premier League.