Barcelona took a 2-1 lead into Wednesday's second leg at the Camp Nou - an advantage extended by Ivan Rakitic's 31st-minute strike in a 1-0 win on the night, as Argentine superstar Lionel Messi reached his imperious best for the hosts.
Luis Enrique's side would have won by a far bigger margin but for a magnificent display by City goalkeeper Joe Hart, while they were also spared a nervy finish when Sergio Aguero spurned a 77th-minute penalty.
"I think we lost against a better team without doubt," Pellegrini told Sky Sports.
"Lionel Messi is very difficult to contain. Maybe we didn't play so well in the first half but we improved in the second and we took risks.
"We needed to score two goals and we thought it might happen had we scored the penalty. That was a very important moment because we had 15 minutes more to play."
Pellegrini was widely criticised for taking a cavalier approach when he picked two strikers for the opening leg at the Etihad Stadium and his midfield was comprehensively overrun.
Aguero featured as a lone forward in the return leg - prompting his manager to suggest that tinkering with formations can be futile when faced with the quality possessed by La Liga's leaders.
"We have had four games against Barca and we played with four different formations," he said.
"So [the tactics] were not a problem, it was the performance."
City's defence of their domestic title has faltered badly since the turn of the year and a failure to secure further progress in Europe means Pellegrini's position as manager is likely to remain under heavy scrutiny.
But the Chilean brushed off suggestion that he was feeling the pressure of his situation, and pointed to City's punishments under UEFA's Financial Fair Play (FFP) rules as a mitigating factor in their continental campaign.
FFP punishments meant City could only name a 23-man squad for the Champions League, while their net spending last close season was restricted to €60m.
"All of us wanted to continue, we need to improve in Europe and maybe in the last two years we did improve," he continued.
"We have gone through to the last 16 and we were very unlucky we played against Barcelona, but at least we qualified [for the knockout stages].
"I also think it was not our best year to continue in Europe because of [Financial Fair Play] restrictions with the amount of players and money so it was difficult in that sense."
