Those countries both narrowly secured the required two-thirds support of the 192 voting members of the UN General Assembly on Wednesday's first ballot, while Canada fell short.
Kenya on Thursday evening won the Africa seat at the UN Security Council after garnering 129 votes against Djibouti's 62 votes in the second round of voting.
Norway and Ireland declared their candidacies for the council several years before the Liberals were elected in 2015, after which Trudeau announced Canada's intention to run.
The country along the northeast coast of the Horn of Africa has put up a spirited parallel fight despite African Union's decision to endorse Kenya in order to secure the only seat allocated for Africa.
Trudeau levelled veiled criticism at the UN's geographical organization that has placed Canada in a grouping against European countries, which can never agree on two candidates for the temporary seats on the council.
The five winners will join the council on January 1, 2021, for a 2-year term.
The defeat of the Liberal government effort led by Trudeau followed a failed bid by the former Conservative government under Stephen Harper in 2010.
And instead of voting separately for the next General Assembly president, five new members of the Security Council and 18 new members of the Economic and Social Council, the three elections were held at the same time by secret ballot.
Among the early voters were US Ambassador Kelly Craft and the ambassadors of Poland and Turkey.
Illustrative The UN Security Council holds a meeting at United Nations headquarters
The elections for non-permanent seats of the UN's most powerful are often routine annual events.
She said that the UN Charter has entrusted the Security Council with primary responsibility for the maintenance of worldwide peace and security. India had by last evening won its contest for the Asia/Pacific region, scoring 184 votes.
"We will continue to play a vital role in advancing global cooperation and building a more peaceful, inclusive, and sustainable world".
Trudeau said Canada "listened and learned" from other nations and has "created new partnerships that increased Canada's place in the world".
"He sold out Canada's principles for a personal vanity project and still lost", Scheer said in a statement. "I was hoping we would, and we certainly worked hard to do it". Besides, all members of the Council get a chance to preside of sittings, providing another opportunity to influence agenda.
The number of women on the council will double from two now - US Ambassador Kelly Craft and St Vincent and the Grenadines' Rhonda King - to four when Norway's Mona Juul and Ireland's Geraldine Byrne Nason join in January.
The General Assembly will also elect its president for the 2020-21 session on Wednesday. Greece, Cyprus and Armenia asked for a vote rather than electing him by consensus.
Only one candidate is running, Turkish diplomat Volkan Bozkir.
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