They took the lead in the 14th minute when referee Neil Swarbrick - in a demonstration of the effectiveness of the Goal Decision System - indicated that Edin Dzeko's shot had crossed the line before Kevin McNaughton cleared.
Pellegrini said: "I think we are in a very good moment, and the confidence of the whole team, not only 11 players, is very high at the moment.
"Of course if the season continues in this way in the last month there will be pressure for all the teams.
"I hope we will continue in this way. It will be a very close Premier League until the end."
Pellegrini was not overly concerned about the goals his side conceded.
He said: "It is better to be concentrating but this team is playing very often, a game every three days.
"Cardiff didn't have many chances to score goals. One in the last minute and one play they did in the first half.
"We missed five or six clear goals. It is better not to concede goals but it is not my first worry at this moment."
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