The visitors went ahead after a mistake by Thiago let in Manuel Iturra but the Blaugrana restored parity and then went ahead before halftime.
Ignacio Camacho got 10-man Malaga's second precious away goal to tie the match at 2-2 in the final minutes, but Pellegrini feels on the evidence of the second-half performance his team deserved much more.
"In the second half we surpassed Barcelona in all respects, even in chances created because they barely reached their goal," Pellegrini told reporters. "In the first half we did not play well and gave away a goal to Barcelona. They had been better then.
"The tie is now open. If we play like we have in the second half here in the Champions League last 16, we may be able to progress in that competition."
Malaga faces Barcelona in the second leg of the quarterfinal with the encounter with Porto in the knockout stage of the Champions League on the horizon.
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