Merkel, during a campaign in Germany's southern state of Bavaria, said following the election of Trump and Brexit, Europeans "really have to take destiny into their own hands".
"We Europeans truly have to take our fate into our own hands", she added.
Merkel also complained after the meeting that there was resistance during the summit to drafting language that would have called for more measures to help refugees.
Germany and other European nations were unimpressed with Trump's performance at both the North Atlantic Treaty Organisation and G7 summits last week, where he refused to endorse NATO's collective defense principle or the Paris climate agreement.
The sharp words from Foreign Minister Sigmar Gabriel came after Trump concluded his first official tour overseas that took him to Saudi Arabia, Israel, Brussels and then Italy for a G7 summit. "The figures speak for themselves", she said.
Trump's run-ins with Merkel at the back-to-back summits injected the United States president into the German campaign ahead of the country's September 24 election.
PM Modi and Merkel had a walk in the grounds of Schloss Meseberg, the official state guest house of the German Chancellor.
After the summit, Ms Merkel called the climate talks "very hard, if not to say, very unsatisfactory".More news: Bihar Board BSEB Intermediate Class 12 Results Expected Today At Biharboard
The frustrations began in Brussels when Trump renewed his attack on Germany's trade surplus and auto exports in a private meeting with European Union officials.
Merkel assured Monday she's still willing to work with the United States - if Trump can take her criticism.
At the alliance's meeting on Thursday, Trump lambasted 23 of the alliance's 28 members - including Germany - for "still not paying what they should be paying" towards the funding of the bloc. His failure to voice clear support for NATO's mutual defense doctrine, Article 5, and to evoke Russian Federation as NATO's prime threat also irked Berlin and other allies.
Merkel described the climate discussion in Sicily as "very dissatisfying".
Merkel's comments underscore a creeping geopolitical shift after G-7 leaders failed to convince Trump to stand by the global Paris climate accord.
Trump's refusal to give allies any indication of whether he would stay in the Paris climate agreement left a bad taste.
There are more than 1,600 German companies and 600 German joint ventures in India and the German economic profile supports excellence and expertise that match with India's development priorities of Make in India, Clean India, Skill India, Digital India, Smart Cities, the MEA said.
Earlier, ahead of his visit, he had said in a Facebook post, "I am confident that this visit will open a new chapter in our bilateral cooperation with Germany and further deepen our strategic partnership".