Celtic booked a third-round qualifier against Legia with a 5-0 aggregate victory over KR Reykjavik last week but Collins insists the Polish champions will be a huge step up in class on Wednesday evening.
Speaking as the squad flew out from Glasgow Airport, Collins told Sky Sports News: "There is no doubt this will be a very tough match.
"We watched them against St Pat's in Dublin last week. They scored five goals, they're a good team but at this stage of the tournament you are not going to play against any mugs.
"I think there is no doubt that they are a step up in quality from Reykjavik. They are organised, quick and score goals and we are going to have to play well against them."
But Collins is hopeful Celtic can emulate the heroics of Neil Lennon's side by reaching the group stages for the third successive season.
"I think we are getting fitter now," he said. "That's another hard week's training we have under our belt and the boys have trained really well and are looking sharper as every day goes by.
"We know it will be tough. They are Polish champions and they've spent money on strengthening their squad, but the squad we have is capable of reaching the group stages.
"Obviously we would like to add to the squad but we have plenty of good players at this club. The challenge now is to qualify for the Champions League. That is the big time and that is where we want to be."
And Celtic's latest recruit, Jo Inge Berget, is desperate to play his part in helping Collins, and manager Ronny Deila, book their place among the continent's elite.
Berget, a compatriot of Norwegian boss Deila, joined Celtic on a six-month loan deal from Cardiff on Monday and has flown to Warsaw with the remainder of the squad.
"The Champions League was a huge part in my decision to come to Celtic," he said. "I have been in the qualification stages twice before but never reached the group stages so hopefully we will get there.
"Whether or not I make my debut in Warsaw is not up to me, but I am able to play. Things didn't work out for me in Cardiff and I didn't play as much as I wanted to, but hopefully it will turn around for me at Celtic."
Watch all the action from the group stages of the Champions League on Sky Sports 5 - the new home of European football which launches on August 12.