Spurs outplayed the Blues on Sunday and left Goodison as 6-2 winners, but Coleman and co. responded superbly to record a 5-1 away victory at the Clarets in their next game.
Speaking to Press Association Sport, Coleman said:
“We wanted to bounce back after that very disappointing defeat to Tottenham. We knew it was going to be tough because they [Burnley] cause a lot of problems for teams with their style of play.
“Our three centre-halves dealt with it brilliantly throughout the game, then we had that little bit of talent in the forward positions to cause them trouble so we’re very happy with the win.”
It has been a particularly difficult season so far for Coleman, who has received a fair amount of criticism for his performances down the right flank.
But the 30-year-old spoke of how Blues boss Marco Silva has continued to encourage him and his team-mates constantly, despite his personal lack of form and a run which saw Everton go five games without a win, adding:
“The confidence was there. The manager keeps telling us to believe in ourselves, to keep playing with a smile on our faces. At times we did that.
“I thought there were periods in the game where we were very good, periods where we weren’t so good but it’s a work in progress and we want to keep getting better throughout the season.”
On the other side of the pitch, left-winger Bernard was outstanding at Turf Moor, managing two assists as the Brazilian caused havoc throughout the game.
The diminutive wide man, signed by Silva on transfer deadline day in the summer, was singled out by Coleman for specific praise after one of his best individual showings in his early Everton career:
“If you watch training, he causes our defenders problems every day. He’s a very talented, very special player and we’re very happy to have him at the club. He’ll only get better throughout the season as well.
“I’ve played with some quality players here in the past but this group, taking it on its own, there’s some very good players and some very talented players, and very good people, which is important if you want to be successful.
“The lads in the team that we’ve signed have been great characters so let’s just see how the season goes and try to finish as high as we can.”
With a seemingly kinder run of fixtures next up for Everton, starting with a trip to Brighton & Hove Albion on Saturday, Coleman sees this period of the season as crucial, and believes the Toffees must now build on their Boxing Day success:
“We had a little run earlier in the season against teams below us in the league where we went on to win some games but it’s an old cliche, and it’s true, there are no easy games and you’ve got to take each game as it is and be prepared because every team causes their own problems.”