A first-half double from Liverpool loanee Rhian Brewster and an Andre Ayew penalty put the visitors three goals ahead inside 34 minutes, yet the Swans could have scored more in a one-sided first half.
The second 45 minutes was less eventful, as neither goalkeeper was really tested after the interval.
In his post-match press conference, which was held via a video link on Zoom, Cooper said: "3-0 away from home is a fantastic result at any time of the season, never mind having not played for as many months as we have and having little preparation to get ready for the game.
"To go 3-0 up as quick as we did having missed two easier chances is very pleasing. It gave us a brilliant foundation to get a fantastic result.
"I can't say I loved too much after the third goal to half time. We didn't quite get up the pitch enough but we still tried to play and legs were getting tired. We defended a lot of long balls and set plays but we were good for the clean sheet.
"It's obviously a fantastic result and a great restart for us, but there's still stuff we want to improve on. That'll always be the case. It's important you enjoy victories like this away from home."
Cooper went on to praise Brewster’s performance, while admitting the 20-year-old was desperate to score a hat-trick.
The Swansea boss also singled out lively wingers Aldo Kalulu and Andre Ayew, as well as Chelsea loanee Conor Gallagher who caused Boro problems in the number 10 position.
When asked about Brewster, Cooper added: "He looked a real threat, got his two goals and he's disappointed he didn't get three.
"He's a really good player, but we are a team that likes to play as a team. Aldo was equally a threat down the right hand side in the first half and Andre doing what he does. I thought Conor Gallagher did brilliantly and even the midfield players getting high up the pitch.”