Fallin's comments came Monday, the day thousands of teachers rallied at the state Capitol seeking increased spending for the classroom.
It also retweeted support for teachers in Kentucky.
Fallin said the corrections and health and human services also need more money.
Chisholm teacher, Karen Smith, explained why they marched saying, "They put the raises through but no funding, that doesn't work".
A teacher told Buzzfeed News, which she's been buying textbooks for her students: "I'm funding my classroom, which is great, but I need them to now step up in order to do that".
"We're madder than hornets, and the hornets are swarming today", said Claudette Green, a retired teacher and principal.
Six involved an elementary school student which 15 involved kids in middle school. The spending and taxing proposals cleared the Senate on Monday.
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As the state Legislature failed to pass funding increases that met that high burden over the a year ago, discontent grew among Oklahoma school districts.
"Their success has shown us that collective activity can work", Kentucky teacher Corey Sayre said of the West Virginia walkout. These funds aren't enough to survive on in many communities, and that reality is understandably encouraging some teachers to apply for positions in other states where the pay is better.
Last week, the Republican-controlled legislature passed a tax hike to increase teacher pay by an average of $6,100.
Teachers picket around the Oklahoma State Capitol in Oklahoma City on Monday.
Union officials did not immediately return a phone call seeking comment. But some educators - who haven't seen a pay increase in 10 years - say that isn't good enough and walked out.
Oklahoma's three largest school districts, Oklahoma City, Tulsa and Edmond, will remain closed Tuesday to honor the walkout.
Adjusted for inflation, the amount the state spends per student has fallen almost 30 percent over the past decade, according to the left-leaning Center on Budget and Policy Priorities.
They were following in the footsteps of teachers in West Virginia, who walked out of class last month and were able to win a pay raise.
Oklahoma City Public Schools announced its campuses would be shut through Tuesday.
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Oklahoma teachers rank 49th in pay and haven't received a raise in more than a decade.
Education advocates and teachers have filled the Capitol to capacity and troopers are limiting access to the building. But some districts not on break had to cancel classes because of teacher absences.
She said that applies as well to how Republicans waited until Monday morning to roll out a budget and a revenue bill which significantly alters the state's tax code and then scheduled votes on the bills for the same day.
Amanda Carter, a middle school teacher from Rowan County, says the plan doesn't provide the same security as the conventional defined-benefit pensions now received by teachers. But the end of the school year is quickly approaching - and the end of the legislative session is, too. But Monday's event is shaping up as their biggest event as lawmakers try to reach agreement on a new budget.
Educators say years of austerity in many states have led to wage stagnation and the hollowing-out of school systems.
The wave of strikes in Republican-dominated states, mainly organized by ordinary teachers on Facebook, has caught lawmakers and sometimes the teachers' own labor unions flat-footed.
Red Dirt Report's M. Tim Blake was at the State Capitol and took a series of photos of the rally attendees, who participated with a mixture of humor and determination. We don't play, play!
A vocal crowd inside the state capitol rotunda in Frankfort chanted "public schools!" and sang "We're not going to take it anymore" as legislators began their workday.
Martin County originally planned on using Monday through Wednesday of spring break as make-up days, but now the district has chose to cancel those three days for the teacher rallies.
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Mireille Knoll lived alone and was found dead after a fire broke out in her flat in Paris's 11th arrondissement on Friday night. In January, a Jewish High School girl's face was slashed on her way home and an arsonist burned a kosher grocery.
Furious over what many teachers are calling a "bait and switch" tactic, Kentucky educators aren't only protesting the pension bill, they are demanding more school funding.