The Airtricity Premier Division league leaders secured a late draw in Vilnius in the first leg and will be seeking to make their home advantage count in the return leg
Buckley told the club's official website that he is expecting a tough tie in Dublin, but believes his side can progress. "Zalgiris are a very good side and the players would back that up having played them in their home ground last week," he said. "They are a good side along the lines of Siroki Brijeg who we played last year.
"That was also a draw in the first leg and we found the second leg to be tough so we know that this return game against Zalgiris will also be a real challenge. But from our end of things, we've been working well this week in training so we're hopeful we can get through."
Pat's currently sit at the top of the Airtricity Premier Division table, and Buckley is hoping that a big home crowd can inspire his side to victory.
"The players have really been boosted by our support this year and I can tell you that they really appreciated the support they got in the first leg," said the Saints boss. "Richmond is a really special place on European nights and can really be a big advantage to us on Thursday if the crowd get behind us on the night.
"Fingers crossed we'll see big numbers turn up for the game and we can give the supporters something to shout about."
Zalgiris coach Marek Zub knows his side will probably need to win to progress, but is not worried about St Pat's being considered favourites. "You should not write us off, we can win," he told Lrytas.lt.
"We have learned from the first game. Now we know our opponents, we know their weaknesses. We have to play a little differently. We have to be cautious and not be as open as in the first leg."
A win for St Patrick's Athletic would set them face either FK Teteks of Macedonia or Pyunik FC of Armenia in the second qualifying round on July 18 and 25.
The Saints host Zalgiris at Richmond Park in the second leg of the Europa League first qualifying round on Thursday July 11. Kick off 19:45 BST.