The Scottish side made heavy weather of seeing off Hapoel Be'er Shiva, but the manager insists that the club belong among Europe's elite
Having secured a 5-2 win in the home leg of their qualifying play-off last week, the Scottish champions found the Israeli side a very different proposition at Turner Stadium and were grateful to goalkeeper Craig Gordon for saving a first-half penalty as they hung on grimly to claim a 5-4 aggregate victory.
After Mahran Radi saw his early spot-kick kept out by Gordon, former Chelsea striker Ben Sahar headed the hosts in front on 21 minutes.
And Romanian midfielder Ovidiu Hoban duly doubled Hapoel's lead when he took advantage of a comical defensive mix-up between Gordon and Saidy Janko to side foot home from close range three minutes after the break.
Scott Sinclair and Moussa Dembele then both wasted great chances to halve the deficit and ease their side's nerves during the second half.
But while acknowledging that his charges were not at their best, Rodgers was still quick to praise their resolve.
"It was the longest 90 minutes I've had as a coach," he said. "Be'er Sheva were outstanding.
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"They had to force the game and they played very well, but I have to congratulate my players. All the work we have done over the course of pre-season has been around that mentality and quality.
"It was an amazing effort by the players on the back of everything they have been through.
"When I came in, the criticism was that Celtic couldn't tough it out, but we showed over two games under huge pressure, that this team can. I'm delighted they have got their rewards."
Rodgers went on to outline what Champions League qualification means for the Glasgow club, who had missed out for the previous two seasons.
"I'm proud firstly for [major shareholder] Dermot [Desmond], [chief executive] Peter [Lawwell] and the board; it's great for them," he said.
"They stuck their neck out in the summer. The club has a real positive feel to it and this is hopefully going to keep that momentum going. It's a huge step for us
"Then obviously there's the supporters. It's an incredible moment for them. They're back in Europe's elite - where Celtic belong.
"So much was riding on this qualification and as you say, this was typical Celtic. But it's really happened; we've qualified."
The draw for the Champions League group stage will take place on Thursday, with Celtic returning to domestic action on Saturday when they host last season's league runners-up Aberdeen.