Bellerin suffered a right thigh injury at Selhurst Park and will be assessed ahead of Liverpool's trip to Emirates Stadium on Saturday - where a win would move Arsenal to within one point of Jurgen Klopp's side.
Emile Smith Rowe made it 2-0 in the 50th minute as he bundled home Carl Jenkinson's cross.
Young Frenchman Guendouzi was then dismissed for a second booking in the 56th minute after needlessly tugging on Jordan Thompson, and Paudie O'Connor pulled one back soon after.
Blackpool pressed for a leveller but their hopes of a fight back were dashed when O'Connor was sent off for a challenge on Pierre-Emerick Aubameyang.
"He's playing well. He's playing with a spirit - [he's] competitive".
The English League Cup match between Arsenal and Blackpool will be broadcast live on ESPN+.
"I don't know if it's experience".
'A red card is like that. Competitive. The action is... it's an action, he plays that action as a normal moment in the game, ' said the Spaniard.
"We are looking for the confidence in each goalkeeper". His quality for the team, I am going to prepare with other players for the big match.
The Tangerines were looking unsafe after halving the arrears, Nathan Delfouneso having a goal ruled out for offside after Petr Cech had been caught in possession. "I have many good memories, so I miss them".
"As a manager you have an influence, not only on the careers of players, the style of play and results but on the structure and impact you give to the club and overall that is very important - that the club can always continue at a very good level".