Python - Add Missing Data to New Dataframe

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I am comparing two dataframes by looping through both and determining if data (row) from one does not exist in the other. If there is no match, I want to add that specific row to a third dataframe. I was able to achieve this with the append() method, but Python warns me that it is deprecated and tells me to use concat instead. Unfortunately, I cannot get concat to achieve the same result.
import pandas as pd

df1 = pd.DataFrame(
{
"Animal": ["Corgi",
"Labrador",
"Orange Cat",
"Black Cat"],
"Owner": ["Bob",
"Joe",
"Sara",
"Glen"]
})

df2 = pd.DataFrame(
{
"Animal": ["Corgi",
"Labrador",
"Black Cat"],
"Owner": ["Bob",
"Joe",
"Glen"]
})

dfF = pd.DataFrame(columns=["Animal", "Owner"])

if df1Sort["Animal"][ind] == df2Sort["Animal"][subInd]:
print("Found match:",
df1Sort["Animal"][ind],
"-",
df1Sort["Owner"][ind])
break
print("No match for:",
df1Sort["Animal"][ind],
"-",
df1Sort["Owner"][ind])
break

print(dfF)

import pandas as pd

df1 = pd.DataFrame(
{
"Animal": ["Corgi",
"Labrador",
"Orange Cat",
"Black Cat"],
"Owner": ["Bob",
"Joe",
"Sara",
"Glen"]
})

df2 = pd.DataFrame(
{
"Animal": ["Corgi",
"Labrador",
"Black Cat"],
"Owner": ["Bob",
"Joe",
"Glen"]
})

dfF = pd.DataFrame(columns=["Animal", "Owner"])

if df1Sort["Animal"][ind] == df2Sort["Animal"][subInd]:
print("Found match:",
df1Sort["Animal"][ind],
"-",
df1Sort["Owner"][ind])
break
print("No match for:",
df1Sort["Animal"][ind],
"-",
df1Sort["Owner"][ind])
break

print(dfF)

The output is:

Found match: Black Cat - Glen
Found match: Corgi - Bob
Found match: Labrador - Joe
No match for: Orange Cat - Sara
Animal Owner 0
0 NaN NaN Orange Cat
1 NaN NaN Sara

Found match: Black Cat - Glen
Found match: Corgi - Bob
Found match: Labrador - Joe
No match for: Orange Cat - Sara
Animal Owner 0
0 NaN NaN Orange Source of the question:

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