City have never progressed further than the semi-finals of the competition, reaching that stage in 2015-16 before losing to eventual champions Real Madrid.
"I think the expectations, you have to win it on the pitch," Guardiola said after City beat Fulham 3-0 in the Premier League on Saturday. "So I think I am not concerned for one second [with he idea that] we deserve more credit for the Champions League.
"I spent many times and we analysed that many times and I can tell you from history we don't deserve it because still we didn't make an exceptional year in the Champions League. We did it in the group stage. But that is not the issue, that is not the problem. In the end the sentence is on the pitch.
"We can talk: 'We deserve credit, we deserve credit, we are favourites, we are favourites'. It's Tuesday, Wednesday Champions League games, show me the money, guys.
"You know, we deserve credit because we deserve it or we arrive in some situations in knockout games and have influence on something you can't control, make an influence but it is what it is. In the end we got to the quarter-finals and we didn't go through but we deserved it. We will try to do better this season.
"I don't feel under pressure to win the Premier League. I didn't feel it last season or two years ago. I want to see us play better without mistakes with simple things. That is what I want and after the sentence, on the pitch, on the grass, that is the real judge."
Buen triunfo con un gran clima en el Etihad. Gracias a todos por el apoyo y a concentrarnos en el miércoles//Great win and atmosphere at the Etihad. Thank you all for the support and getting ready for Wednesday. C'mon City!! pic.twitter.com/zZCTR7BZb4— Sergio Kun Aguero (@aguerosergiokun) September 15, 2018
Although City eased to victory against Fulham thanks to goals from Leroy Sane, David Silva and Raheem Sterling, Guardiola was unimpressed with certain aspects of his side's showing and cited a poor miss from the otherwise exceptional Bernardo Silva as a source of frustration.
He said: "Maybe it was the reaction of when the ball got passed to Bernardo and I said it is impossible that he is going to miss it because of his quality but he missed it and I said 'wow'. My reaction and extra expression is when they miss the simple things. That, I cannot handle in myself.
"So one guy has the ball and they miss the ball and an extra simple pass, an extra touch, an extra touch and after miss the pass, that is why I... still now I am angry. I am upset with my players and they know that. We spoke about that many times.
"About missing the goals or about the assists or a shootout... dribbling, go one against one, two against... and lose the dribbling, it doesn’t matter, but control the ball and pass the ball simple, if they miss that, and today there was a lot of that, that’s why I am going to show them we can improve.
"They [the players] are maybe angrier than me so no doubt. We speak many times, pass the ball two or three metres, don't miss that ball and today it happened a few times especially in the first half and the teams that want to play in the top level they punish you a lot.
"But normally that happens after international breaks this kind of thing happens, it can happen, with the travel, one training session, play. You are still not [doing] the normal situations. Now we start. Every three days until the Liverpool game we will be here for one month with a game every three days, so everyone is going to settle."