"You can see a tremendous sense of togetherness and spirit and we have quality to go with it, and when you bring that to a football match you have a great chance," Coyle added.
"We want to entertain but you have to win the games while you are doing that.
"We know every bit of hard work that is ahead of us. But I know the drive and desire of my players.
"We asked the players to give the same again, and from the first whistle the level of performance was terrific. If I'm nit-picking I'm disappointed we lost a goal but Newcastle are a good side with good players."
Coyle was particularly delighted for Elmander, whose brace came two days after his wife gave birth to a baby girl.
He took his tally for the season to eight, and Coyle is confident the Swede will sign a new contract at the club.
"I knew Johan would be chomping at the bit to play today and his performance was outstanding," said Coyle.
"I'm very comfortable with the relationship I have with Johan. We speak all the time and I understand that as a player you get on a run and you don't want to be sidetracked. We'll continue to have a dialogue and it doesn't faze me."
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