Begovic's shut out in Saturday's 1-0 win over Arsenal was his first since the goalless draw at Hull 15 fixtures ago.
"It's always great to get a clean sheet," the big Bosnian told The Sentinel.
"I feel that one has been coming for a while, but we just haven't had the luck that we would have wanted in recent weeks.
"Our defensive organisation and performances have been more than okay, but we just haven't quite been able to get that clean sheet until now.
"It was a fantastic performance, we really stuck together and we were able to get the clean sheet and the win."
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