Greater Manchester Police's Chief Constable revealed the force attended 126 incidents over the weekend.
Officers were slammed by some for breaking up the child's party in Manchester and issuing a fine.
But Ian Hopkins said it was not a "jelly and ice cream" event and saw "mostly adults celebrating".
Police were "in a difficult position" with "lots of reports" of lockdown breaches, he said, and were trying to take a "very balanced and proportionate view".
He continued: "We can't win. If we don't deal with them, people are saying it isn't fair and when we do deal with it people are saying it is heavy-handed.
"Throughout this pandemic we have issued very few fixed penalty notices. And even this weekend we have only issued 19.
"We don't get to everything. We just have to assess which [gatherings] appear to be the biggest and most problematic."
Lockdown restrictions on social gatherings remain in Greater Manchester following a local spike in cases.
As well as illegal gatherings, officers visited 172 licensed premises over the weekend.
Mr Hopkins said "pretty much all" bars were showing "really good measures to keep people safe" but that was not the case with house parties.
"It isn't safe. Social distancing is not taking place and that will lead to the virus spreading," he said.
He said the force had received help this weekend from police forces in Durham, Humberside, North Yorkshire, Cheshire and North Wales.
He said it meant an extra £100,000 a week had to found to cover the costs.
The child's 10th birthday party in Swinton was being attended by three families in a private garden after 20:00 BST on Friday.
Mr Hopkins said the force was not "making an example of them" but defended the fine issued to the homeowner, adding: "Those people knew they were breaching the regulations".
The party's host declined to comment when approached by the BBC.
Officers were also called to what turned out to be a party for a terminally ill child.
Mr Hopkins said officers used "discretion" and "had a quiet word" with the host before leaving.
In the end, a vision without the ability to execute it is probably a hallucination.