Celtic will not play in the group stage for the first time under Rodgers after losing 3-2 on aggregate to AEK Athens.

There have been reports of unrest between Rodgers and the board over a failure to sign several targets.

After Tuesday's 2-1 defeat in Athens, he said the club had to "always guard against becoming complacent".

"You do that by adding to the squad," Rodgers told BBC Scotland. "It's pretty obvious, you have to keep progressing and keep getting stronger."

Referencing his former club, he added: "You only need to look at Liverpool, who got to the Champions League final and invested the money they had to be stronger."

Celtic made about £30m after reaching the Champions League last season, and stood to earn more this term after Uefa announced a 50% increase in prize money.

Instead, AEK will play Hungarian side MOL Vidi for a place in the group stage, with Celtic dropping into the Europa League play-off round.

Rodgers' side will face either Latvia's Spartaks Jurmala or Suduva of Lithuania, with the prize money for winning that tie £2.6m, compared to £13.6m for reaching the Champions League group stage.

'Two moments have cost us'

After a 1-1 draw in the first leg, Rodgers said Celtic lost "two soft goals" in Athens, leaving them 3-1 down on aggregate with 40 minutes remaining.

Brito Rodrigo Galo put AEK ahead after six minutes when he found space in the box to convert a cross, and Marko Livaja added a header just after the break as Celtic failed to deal with another delivery.

Scott Sinclair gave the visitors hope with 12 minutes remaining by heading in, but Celtic could not find a second to edge them through on away goals.

"We gave them lots of problems and over two legs, we felt we were the better team but you have to defend well," said Rodgers.

"Two moments have cost us. We did it against Livingston, Alashkert, Hearts earlier in the season and now we've done it here. Ultimately, that's not good enough."

Kristoffer Ajer was suspended for the visit to Greece, while Dedryck Boyata did not travel, amid suggestions he had refused to play. Rodgers said after the game the Belgian would have been fit to make an appearance.

There were also problems up front, with record summer signing Odsonne Edouard injured and Moussa Dembele fit enough only to be a substitute.

"We've been unfortunate in missing some of our key players," said Rodgers. "We wanted the Champions League but the Europa League is still a very good competition.

"Celtic will always attract very good players and that is hopefully something we can still do before the window closes."

Midfielder Callum McGregor echoed Rodgers' sentiments, saying the dressing room needed "a couple of faces to freshen it up".

He told BBC Scotland: "The teams round about us have strengthened. So if we got one or two in with real quality then the boys would welcome them."

'I can't see them investing now' - analysis

Former Celtic goalkeeper Pat Bonner on Sportsound

I can't see them investing now. I don't think they'll rush in. I think they'll get to the group stage in the Europa League.

I don't see them going out now and buying two or three players at this stage of the season. They have to deal with the Boyata situation, and quickly.

Former Celtic striker Chris Sutton on BT Sport & Twitter

Celtic have stockpiled money. They've spent £2m on disco lights at Celtic Park for Champions League nights. They might not get there. Invest in the playing squad.