Paterson rounded off Huddersfield's 2-0 triumph over Milton Keynes Dons in midweek, and Burke was happy for his Forest teammate.
Paterson is currently on a season-long loan with Huddersfield from Forest, and the hope is that he can continue to impress while with the Yorkshire side.
The 23-year-old remains highly regarded by many at the City Ground, but he has found first-team chances hard to come by under Dougie Freedman.
The Scottish boss has other preferences in his squad to use out wide, and Paterson has had to go out on loan in order to guarantee regular action.
So far during his time at Huddersfield, the former Walsall attacker has played four times, and he will be hoping that his goal against MK Dons will lead to Chris Powell giving him increased starting opportunities.
Huddersfield's next game comes against an in-form Derby County side on Saturday, and Paterson would endear himself further to Forest fans if he is to score against their local rivals in the fixture.