The Hoops’ 3-0 win in Brussels on matchday two meant the visitors had to equal or better that result in their final Group B game to leapfrog the hosts, unbeaten in 67 domestic games, into third place.
A second-half own goal by defender Jozo Simunovic meant Celtic suffered defeat against the Belgian side following losses home and away to European superpowers Paris St Germain and Bayern Munich, who eased into the knockout stages of the Champions League.
Celtic will resume in the Europa League last-32 in February but Rodgers, whose side finished bottom of their Champions League group last season with no wins, predicted even tougher times ahead with regards top-tier ambitions in Europe.
The former Swansea and Liverpool manager said: “It will become even more difficult for us.
“We have to be realistic in terms of European football.
“We are a long, long way behind in relation to budgets and structures and other things at the very top level.
“What we have to try and do is somehow bridge the gap. The club hadn’t qualified for the Champions League for a few seasons, now we have qualified for the last two seasons, which is brilliant.
“We want to make the next step once we have qualified; can we have European competition?
“Of course we want to have Champions League but you have to be realistic. You are not going to finish ahead of PSG and Bayern Munich over the course of games.
“Could we challenge the third place team in the group, Anderlecht, who work on a bigger budget than us and we did that.
“So next year, it doesn’t get any easier, it only gets more difficult.
“So that’s our position and where we are at in the European game.
“We have to somehow develop a way we can maybe bridge the gap and allow us to fight for that second position.”