The Cherries secured their first European home win with goals from Evanilson, Rayan and Álvaro Rodríguez, starting their Europa League home campaign with a result that lifted the mood after defeat at Chelsea.
Cook described the atmosphere and performance as special, saying the players had felt the occasion even before kick-off.
“I thought the performance was top. It was a special night, you could feel that before the game, when were lining up as players. The atmosphere was great. It was a top performance, we bounced back from the weekend and it was something we can be very proud of,” he told TNT Sports.
The midfielder felt the team had handled the quick turnaround well, with little time to dwell on a disappointing result before preparing for another demanding fixture.
“That is a positive. There are so many games in a short space of time. If we have a bad game then we've only got a couple of days to get over it and then onto the next one and I thought the lads showed that today and handled themselves well. It is tough with a bad result to come back and do well. Everyone who played today was fantastic and it was a collective effort and a great win.”
Bournemouth had also made a strong start to their European campaign, and Cook was keen to keep the focus on results rather than the novelty of the competition.
“It is all new to us. All I know is that when you win game sit is good. Hopefully we can use the momentum and carry on.”
Smith, meanwhile, said the occasion had been a long time coming for the club and its supporters.
“It has been a long time coming. The fans were up for it, the players were up for it so we’re very happy with the performance.”
The captain was modest about his part in Evanilson’s opener but full of praise for the striker’s finish. Smith’s delivery led to the Brazilian’s header, which gave Bournemouth the advantage before the break.
“It wasn't my best cross but I put it in an area, what a finish from him and I think we deserved that little bit of luck. From there on we went on to win the game but in the second half we got a little bit tired but the quality that came off the bench is great and we look forward to Sunday now.”
Smith added: “It’s a great header, he deserved it because he has worked very hard this season and many more to come from him.”
After the defeat at Chelsea, Bournemouth’s players had spoken among themselves and were determined to show a different side of their game. Smith said the reaction was encouraging, but insisted the week’s work was not finished.
“Yeah it was very disappointing at the weekend [the defeat at Chelsea], we let ourselves down as players. We had a chat with each other, we got a reaction today. That's an AFC Bournemouth performance right there and the week's not done. We've got a massive one on Sunday against Sunderland and we need to get another three points.”