Midfielder Michael Gault conceded any hopes Portadown had of winning the league ended with Saturday's draw at home to Glentoran.
Portadown took an early lead through Peter McMahon but the Glens hit back to equalise through Jordan Stewart 17 minutes from the end at Shamrock Park.
The Ports are third in the table, 12 points behind leaders Crusaders.
"It is safe to say we will not be catching Crusaders. They are on a great run," said former Linfield man Gault.
"We aim to finish as high as possible and hopefully qualify for European football.
"We have the Irish Cup as well which could be a pathway into Europe.
"But we want to keep picking up points with our next games against Dungannon and Warrenpoint."
Portadown were the better side in the first half against the fifth-placed Glens.
They thought they should have had a penalty for hand ball against Niall Henderson from a Gary Twigg header - but referee Colin Burns did not agree.
McMahon pounced on a mistake by defender Johnny Addis and fired in the opener from the edge of the box.
Glentoran equalised when Kym Nelson flicked on David Scullion's ball and Stewart slid in at the back post to score.
Portadown almost snatched a late winner but Chris Casement's free-kick hit the post.