Ms Smith told the BBC that tougher laws and enforcement were already having an effect.
She said: "This is obviously a tragedy for the family up in Liverpool, and the reason why we need to keep building on the work that we have undertaken to tackle knife crime.
"All of these things are making a difference. Any young person killed in a tragedy like last night is one too many.
"But we've got to carry on with the efforts that we've put in place and to work alongside the community and the police to do that."
Some £2m more was announced earlier this year for the 10 areas, which are London, Essex, Lancashire, West Yorkshire, Merseyside, the West Midlands, Greater Manchester, Nottinghamshire, South Wales and Thames Valley.
Metropolitan Police Deputy Assistant Commissioner Alf Hitchcock, head of the Tackling Knives Action Programme, said the police presence on school routes would target the time of day when trouble could occur between youths.
"Young people tell us that the period after school can be when conflicts arise between different groups and an increase in police presence and in other visible signs of authority can help them be and feel safe and secure," he said.
"This additional funding will assist the 10 Tackling Knives Action Programme forces in further building on the tough approach towards those who carry knives which Acpo [the Association of Chief Police Officers] is leading across the police service."
Shadow home affairs minister James Brokenshire said the initiative was too limited in its scope.
He said: "I support any mechanism that will cut the appalling crimes that we've seen on our streets.
"My concern about this approach is that it's just too targeted. It's saying that the problem is just in certain areas and at certain times of the day, in other words after school.
"Tragically, with the incident we saw last night, it didn't happen just after school and it didn't happen just within the vicinity of the school."
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