Councillor Barrow said the £511,000 saved by withholding the council tax support grant payments would be a vital step towards addressing the "budgetary pressures" at Shirehall.
The authority needs to save £80 million over a three-year period.
But Councillor Barrow admitted the controversial decision – which has sparked anger among town and parish councils across the county – should have been handled differently.
The proposal will go before a full council meeting tomorrow, and councillors have been advised to approve the plan.
A number of councils have increased their precept already, with Worfield and Rudge Parish Council increasing its by 1.99 per cent after losing a £1,000 grant.
Meanwhile, Wem Town Council passed a vote of no confidence in Shropshire Council after it missed out on £30,000 in funding. The council put its precept up by 19.7 per cent after the council funding was withheld.
Shrewsbury Town Council delayed a decision on its budget by two weeks after its annual £78,000 grant was withheld by Shirehall.
Councillor Barrow said it was important to withhold the council tax support grant because of "budgetary pressures".
But he has questioned why town and parish councils have reacted angrily to the proposal when some have got so much money in reserves.
"I don't think we handled it very well," said Councillor Barrow. "We should have sat down with parish and town councils a lot sooner. We have had to make this decision in response to budgetary pressures.
"Shrewsbury Town Council froze its precept, Oswestry Town Council agreed not to increase its and so did Bridgnorth.
"Whitchurch put its up by about one per cent and Wem increased by 19.7 per cent when they have got £400,000 or thereabouts in the bank.
"I don't want to fall out with town and parish councils."
"We are in the second of a three-year plan and we need to make a further £40 million savings by the end of the year," Councillor Barrow said.
"It is going to be difficult and people need to understand while it is difficult now there are more cuts to come.That's what we have got to plan for but hope things turn out better.
"Whoever wins the next election, the spending is going to be the same."
It is not yet known exactly which services may be affected by the latest cuts.