Messi collected his record-extending seventh accolade after more success with Barcelona and Argentina, who ended a 28-year wait for a major trophy with their Copa America win, despite struggling at new club Paris-Saint Germain.
The 34-year-old has scored just once for PSG in seven Ligue 1 outings this term, while Lewandowski has netted 25 times in 20 appearances across all competitions this season for Bayern.
The Poland forward also registered 41 goals in just 29 league games for Die Roten last campaign to break Gerd Muller's 49-year record in a single Bundesliga season, but only finished runner-up at Monday's ceremony.
While coronavirus forced a cancellation of the 2020 Ballon d'Or, which Lewandowski appeared favourite for, Muller feels his team-mate was deserving of the 2021 award as well.
"From a Bavarian, Polish and also from a German point of view, the presentation of the Ballon d'Or yesterday evening was definitely a disappointment," Muller wrote in a post on his official LinkedIn profile.
"For some even a little more. Although I've been in the business for a bit longer and was therefore not really surprised at the outcome (it was similar with Franck Ribery in 2013), the whole thing formed or reinforced a thought in me: We have great players in the Bundesliga and we have to not hide us. However, further international successes are necessary for global recognition.
"This is also a huge motivation for me to put everything into the balance in order to bring the Champions League back to Munich and to show the football world what is going on. And above all, what German football has to offer.
"We have the next opportunity to do so next Wednesday in the Champions League game against Barcelona. Let's tackle it!
"PS: With Lionel Messi, he is probably the best individualist football has ever produced. So congratulations to Lionel on winning the Ballon d'Or, even if I think that Robert Lewandowski would have deserved it more this time."
Manuel Neuer, Thomas Muller, David Alaba and Thiago Alcantara are all out of contract in 2021 and are mulling over the offer of fresh terms from the Bundesliga champions, who extended Hansi Flick's stay as head coach on Friday.
Rummenigge reassured Bayern fans that any economic impact from the spread of COVID-19 would not play a part in how those talks played out.
"Our offers are extremely fair and serious - without a 'corona discount'," he told Bild
"I think that not many clubs around the world handle [it like] this in this crisis."
Flick signed on for three years after impressing in interim charge at the Allianz Arena.
He took over from Niko Kovac in November before being appointed head coach on a full-time basis until the end of the season.
Having appeared in danger of failing to mount a title challenge under Kovac, Flick has since restored the winning habit, returning Bayern to the top of the Bundesliga.
However, he is likely to face a rebuilding job during his tenure as the nucleus of a squad who have inspired a decade of dominance are reaching the end of their contracts.
That was the verdict of Julian Nagelsmann, the head coach who saw his Bayern side prevail 3-2 in a thrilling Klassiker to move four points clear of their closest rivals at the Bundesliga summit.
Lewandowski scored twice for the leaders, the second of those goals a late penalty, in the same week he missed out to Lionel Messi for the Ballon d'Or.
Dortmund fans, who worshipped Lewandowski during his four seasons at Signal Iduna Park, taunted the striker by singing Messi's name while both sides were warming up.
The Poland international took revenge with his double, however, taking his tally against BVB to 26 goals in all competitions – his most against a single side.
Speaking after the game, Nagelsmann said: "All of this rather spurred him on. He scored the significant goals and paid the fans back after all the Messi calls in the stadium."
Bayern were 2-1 up at half-time in Saturday's top-of-the-table clash after Lewandowski and Kingsley Coman struck to cancel out Julian Brandt's early opener.
Erling Haaland hit back for Dortmund, who saw a couple of big decisions go against them in what could well be a defining moment in the Bundesliga title race.
Lucas Hernandez avoided conceding a penalty despite appearing to commit a foul on Marco Reus, shortly before Mats Hummels was deemed to have handled at a corner.
Lewandowski converted the resulting penalty, leading to strong comments being made by the Dortmund camp in regard to the performance of referee Felix Zwayer.
Despite the controversial conclusion to the game, Nagelsmann felt his side were good value for their seventh successive win against Dortmund in all competitions.
"I think we deserved to win, but I also understand the discussions over the two penalty situations," said Nagelsmann.
"It was a very tight game that was worthy of its reputation. We could have scored more in the first half.
"Dortmund did it well early in the second half, but we found our rhythm again and had good control."
Bayern ended the game with an expected goals (xG) return of 2.27 compared to Dortmund's 1.44, backing up Nagelsmann's assertion that his side deserved all three points.
Dortmund had more possession (53 per cent) and outshot Bayern seven to six in the second half, however, and Thomas Muller conceded the visiting side rode their luck in the end.
"Dortmund's first goal has probably helped us," Bayern stalwart Muller told Sky Sport. "We got into the gaps relatively easily afterwards, with the goals scored after mistakes.
"We should have taken the lead in the first half. In the second half, I don't know whether we deserved to win from the way we played.
"The first-half display was definitely better – we moved the ball well and won our challenges. Based on the second-half performance, we didn't deserve it. It was more of a fight."
Head coach Low shocked German football in March 2019 when he announced World Cup-winning stalwarts Muller, Mats Hummels and Jerome Boateng were no longer in his plans.
Muller, who has 100 caps for Germany, said at the time he was "totally dumbfounded by this decision out of the blue".
The 30-year-old has been in fine form since the turn of the year, scoring in four consecutive games for Bayern before Sunday's 0-0 draw with Bundesliga title rivals RB Leipzig at the Allianz Arena.
Some had suggested this could be enough to persuade Low to reconsider his position on Muller, but the Germany coach told Sky on Sunday: "The probability [of a recall] is relatively low if everyone is fit.
"Thomas has scored a few times in the second half of the season. I am pleased, but I said we would go with the young players. That is what we have to maintain.
"However, if things should happen that you do not expect, it is clear you will have to look again."
Speaking after the draw with Leipzig, Muller said: "I'm not interested in it at all. I care about this team [Bayern] and winning trophies with them, ideally three."
Sunday's result means Bayern remain one point ahead of Leipzig at the Bundesliga summit.
The Bayern Munich attacker is the highest-capped player in the squad, moving clear of Jurgen Klinsmann as the sixth-most capped player in Germany's history with his 109th appearance last time out against Liechtenstein, scoring twice in the 9-0 win.
Muller has worn the armband for Germany on a handful of occasions previously, but this would be the first time under new boss Flick, who believes the 32-year-old's presence on and off the field make him fully deserving of the honour.
"Thomas isn't someone to push himself into the spotlight; he prefers to support the team and fire the lads up," Flick said ahead of the game against Armenia. "He is also incredibly important off the pitch because he pushes the group again and again.
"He's a really important player for us, and he'll captain the side against Armenia. I'm happy to have him as a player because he's very, very valuable."
Regular captain Manuel Neuer is rested and therefore does not travel with the squad, missing out alongside Marco Reus, injured pair Leon Goretzka and Julian Draxler and the suspended Antonio Rudiger.
As a result, Muller is given the chance to captain the side, while Marc-Andre ter Stegen has the opportunity to feature between the sticks as Germany look to end their World Cup qualifying campaign strongly, having won eight of their nine games so far to sit nine points clear at the top of Group J.
"Marc-Andre ter Stegen and Kai Havertz will both start the match," Flick continued. "We have already shown in the last few games what quality and mentality the team has.
"Armenia are very strong on the counter-attack, so we'll need to be very alert in defence. Our aim is to end this year with a win, of course."
Defender Christian Gunter is also relishing the chance to stake his claim for a spot in Flick's final World Cup squad next year.
"For me, it's about putting in a good performance for the team," Gunter said. "I'm part of a real competition for places and I want to give Hansi a tough decision when he comes to name his national team squad."
Robert Lewandowski's long goalscoring streak ended at 15 consecutive Bundesliga games – one short of Gerd Muller's record – but the champions moved three points clear of Wolfsburg.
That is now 40 goals in their past eight matches for ruthless Bayern, who led 2-0 courtesy of great finishes from Muller and Kimmich at half-time.
Benjamin Pavard was given his marching orders for a professional foul on Jeremy Dudziak early in the second half, but a Sebastian Griesbeck own goal extended their lead.
Cedric Itten's header in the closing stages was too little, too late for bottom side Furth in the Bavarian derby at Sportpark Ronhof on Friday.
Muller, who also scored the opener in recent victories over Barcelona and Hertha Berlin, is now on 218 goals for Bayern, one more than Karl-Heinz Rummenigge.
Neuer was delighted for his long-time team-mate, although he joked the forward could be summoned to a meeting with the former Bayern CEO after taking his place in the all-time list.
"He doesn't get tired and has been around for a long time," Neuer said, as per Bayern's website.
"I've accompanied him for long stretches of this time, and I'm always happy about every one of Thomas' goals and celebrations, which sometimes look a bit weird with him.
"I'm especially happy for him personally, because we've been playing together for a long time, but I think he'll have to report to Kalle [Rummenigge] today."
Bayern, who next face Dynamo Kiev in the Champions League on Wednesday, have started the season with eight consecutive victories under coach Julian Nagelsmann.
Neuer himself added: "It looks quite good. We scored three goals and showed a good attitude. In the first half, we didn't make enough of it when we had space. We wasted a lot of chances. That's annoying.
"Despite being a man down, we made it 3-0, which gives you a good feeling. Then we got in between the lines better, but sometimes we were too sloppy.
"It's nitpicking really, but we can still play more flowing football. We're happy with how it's going, but we always have to take the next step and improve."
