Having been beaten 1-0 by Southampton in their opening game, the Baggies picked up their first point of the campaign following a hard-fought stalemate at Goodison Park.
Clarke was pleased with the spirit shown by his players, telling Sky Sports: "I said to the boys it was nice to see West Bromwich Albion back. The first game was disappointing but I think we played very well.
"This is a difficult place. Everton are a good team, but we showed today that we are also a good team.
"We had to dig in and defend properly, and with a little bit more quality on the counter-attack we could have created more opportunities than we did, but we still had one or two opportunities that on another day we could have scored."
Nicolas Anelka was absent after being given compassionate leave following the death of his agent Eric Manasse, and it remains uncertain whether the Frenchman will reconsider his decision to retire from football.
There has been a lack of cutting edge in West Brom's first two games but Clarke says he has faith in the players at his disposal and doubts whether he will bring in anyone else regardless of what happens with Anelka.
"I am not sure to be honest," he said. "I think the three boys we have got, Markus Rosenberg, Shane Long and Matej Vydra, are good and all have goals in them.
"The goals will come. That doesn't concern me.
"Today was about digging in and getting a good result, but I think we played a lot of good football too."
Clarke also expressed concern about the fitness of goalkeeper Ben Foster after he had to be replaced by Luke Daniels in the second half, although the extent of his foot problem will not be known until a scan has taken place.
"It's obviously serious because he came off during the game and Ben is not the type of player who would do that if he didn't think something was wrong," said Clarke.
"He said he felt a little pop in his foot, but until we get the medics to look at it and scan it then it is only conjecture as to what is actually wrong with him."