During a visit to Glasgow the Labour leader and his Scottish counterpart, Anas Sarwar, spoke to some nurses working and helping patients with the virus in the Queen Elizabeth University Hospital.
Prime Minister Boris Johnson previously said a delay in deliveries from India, as well as the need to retest a batch of 1.7 million doses, will be behind issues with vaccine supply in April.
And Scottish First Minister Nicola Sturgeon has said the delay means Scotland will have 500,000 fewer doses over the next month than anticipated.
Sir Keir told the PA news agency: “I think the delay in vaccines is a cause for concern.
“The vaccine rollout has been very good and all tribute to those on the front line.
“I hope it can be resolved and I say that in a constructive spirit – nobody wants to see this not succeed.
“So we need transparency from the government, we need clarity about what needs to go right.”
Sir Keir asked nurses how they had managed during the pandemic but praised the different hospital teams for coming together, mentioning his wife’s hospital had only concentrated on coronavirus patients for a while.
Sir Keir’s wife, Victoria, works for the NHS.
When he asked nurses what the mood was like in the hospital, one said we’re “kind of hopefully seeing the end of Covid, it’s on the up and up definitely”.
The Labour leader recognised case numbers are coming down and expressed his hopes the vaccine rollout can continue as “the light at the end of the tunnel”.
Some of the nurses said they had received their second dose of the vaccine, adding staff have been excited ahead of receiving their doses.
The process was described as “slick” by one nurse which Sir Keir agreed was “incredble” before delving into his own experience of receiving the vaccine last Sunday.
Mr Sarwar asked how the pandemic had impacted the nurses’ families, with one replying that despite living alone she had “bubbled” with her parents. However, she could go “two months without seeing them” depending on what areas of the hospital she was working in.
The newly-elected Scottish Labour leader also joked Sir Keir was taking “full credit for bringing the sunshine” to Glasgow with him.
It marks the second day of Sir Keir’s trip to Scotland, having visited a vaccination centre in Edinburgh on Thursday.