Mr Barnier said: “It is true that the UK has a quicker vaccination rate compared to the EU.
“But the fight against Covid-19 is more than the speed of vaccination, important as that is.
“We will all find stronger and weaker points in how we managed this.
“But there is no place, in such a serious situation, for polemics and competition.
“There are so many more reasons to cooperate, in the short and the long term.”
It is not the first time the former Brexit negotiator has appeared to criticise some of the Commission’s actions under Ms von der Leyen’s reign.
The Commission’s decision in January to block vaccine exports across the Irish border by triggering an emergency provision of the post-Brexit deal “was a mistake”, according to Mr Barnier.
The EU went back on its decision to trigger Article 16 but Mr Barnier warned it could have political consequences.
Taking to Twitter, Mr Barnier wrote: “Last day at @EU_Commission where I worked with so many dedicated and talented colleagues. Thanks to all.
“Without nostalgia, also a good moment to reflect on this experience at the Churchill Europe Symposium.”
In his speech in Zurich at the Churchill Symposium on Wednesday he also explained that the reality of Britain’s decision to leave the EU was only now being felt.
Mr Barnier said: “For many people the real consequences of the referendum are only now starting to sink in.
“The reality, which has become clear for all to see, is that Brexit means recreating trade barriers that had not existed for 47 years.”