The phrase 'despite this criticism' is correct and usable in written English.
You can use it when you want to point out that something has been criticized but you still believe it is valid. For example: Despite this criticism, the new policy is the best way to ensure fairness.
Despite this criticism, Poldark received a generally warm reception from reviewers and audiences.
Despite this criticism, and the anger in the south over Mr. Abiola's death, General Babangida said he was confident that General Abubakar would now steer the country to democracy.
Despite this criticism, and despite steep cuts to federal advertising and enrollment-assistance budgets, Americans appear to be signing up for coverage at a faster rate compared with last year.
Despite this criticism, 71percentt of Swiss voters believe their country, which already has Europe's highest concentration of refugees, is attracting too many asylum seekers, according to a poll conducted for Swiss television by the GFS research institute.
Despite this criticism, it should be noted that he made full use of his knowledge of Buddhism to attack Buddhist doctrines severely or to transmute them into his own Vedantic nondualism, and he tried with great effort to "vedanticize" the Vedanta philosophy, which had been made extremely Buddhistic by his predecessors.
Despite this criticism, Kuhn's work has been hugely influential, both within philosophy and outside it.
Despite all of this criticism, historian Gillian Gill describes how Lehzen was honest and frugal; even after Victoria ascended the throne, she seems to have made no demands for money or rank, preferring instead to simply be in the queen's company.
(Moreover, she was critical of The New Yorker and Harper's for printing many more short stories written by men than women). All this criticism despite the fact that most people in publishing believe that more literary fiction is still written by men than women.
Despite this damming criticism from an independent source, the Europe minister, Jim Murphy, valiantly insists that the government has "very strong legal advice that the protocol on the Charter is watertight legally".
Despite this logical criticism, the physical science view of resilience in social-ecological systems became a dominant paradigm, which is well represented through the work of Folke (2006).
No one is supporting this bill". Despite the criticism of Republicans, Ms. McCarthy has won praise throughout her tenure at the E.P.A. for meeting with or listening to a variety of groups, including those in industry, as she drafts major regulations.
