Newcastle, who last won the trophy in 1955, will visit City on March 16 for the knockout fixture.
"I was driving at the time and I almost swerved off the road! It wasn't the draw we wanted, that's for sure," Howe told reporters on Friday.
"I don't think any team wants to play Man City four times in a season. But... to win the FA Cup you will probably have to beat Manchester City at some stage in the competition.
"We are just going to have to do that sooner than we would have hoped."
Newcastle beat City in the League Cup in September but lost to the defending champions twice in the Premier League, where they host Wolverhampton Wanderers on Saturday.
Howe said the return of Elliot Anderson, Joe Willock, Alexander Isak and Sven Botman from injury has given his team a boost.
"At one point we only had 14 or 15 players in the training group, now we have just over 20, so the whole group has been lifted by that.
"The challenge now is to get them all back to fitness as quickly as possible," he said.
"Alex will get there with every game he plays... with Joe, we are trying to nurse him back to full fitness. That will be difficult considering the time he has been out.
"Sven is looking good, we just felt that he would benefit more from training than playing in midweek... we could see him tomorrow," he added.
Newcastle are 10th with 37 points, a point behind Wolves.
