A 2-1 home defeat against CSKA Moscow on Wednesday – when City finished the game with nine men following the second-half dismissals of Yaya Toure and Fernando – leaves Pellegrini's men bottom of Group E with games against Bayern Munich and Roma to come.
That means City – yet to win in this season's competition – look likely to require two victories in the remaining two group games to have any chance of reaching the last 16 and even that might not be enough.
Pellegrini is in the spotlight as City have lost three of their last four games in all competitions and Tueart - who scored the club's winning goal in the 1976 League Cup final – thinks the Chilean's team selections have backfired.
"Well I think it's an all-in responsibility," Tueart told Perform.
"The manager picks the team, he has to assess the opposition, decide what their strengths and weaknesses are and select his team accordingly, and unfortunately in the last couple of years, at the Champions League level with the manager, he's fallen short in both elements.
"What's come through after the last few games - Newcastle, West Ham and CSKA - is two things. First of all, team selection has to be analysed -- whether the team selection we're making is suiting the quality players that are in the team -- and secondly, without question, the value of David Silva, I mean that has been possibly not valued as great, but without him we are a different side.
"Yaya [Toure]'s performances have been a little disjointed, but I always go back to the [Roberto] Mancini reign when Yaya was at his marauding best, when we played a team selection of two holding midfield players with Nigel de Jong and Gareth Barry allowing Yaya to use his element of attacking force, and his power, and his ability to get forward, without any real defensive responsibilities, with having those two holding midfield players.
"And we very rarely had that team selection again since and it mystifies me why that's not happening.
"I think you have certain levels of qualities when you're a Premier League club. You have the domestic trophies, you have the Premier League competition and you also have the Champions League.
"In each stage, there's a grade above the previous stage, and I think we've acquitted ourselves very well in the Premier League, but in the Champions League we haven't been able to sort of get our strategy right, our team selection right, our attitude right.
"All the things you need when you're playing in the next stage of quality level."
He added: "When the owners look at the amount of money they've invested in the squad, individual salaries, and individual price-tags, they're quite entitled to expect a better performance and I would sort of understand where they're coming from and say 'we need to address this very quickly'."
