Former Real Madrid manager Arbeloa was denied his first win in the English top-flight in painful fashion as Fulham conceded twice in the final moments at Portman Road.
Ryan Sessegnon's 55th-minute strike for Fulham was cancelled out by Abdoul Ouattara's long-range rocket in the 88th minute before Dara O'Shea headed home in stoppage-time.
Fulham are mired in the relegation zone as questions mount about Arbeloa's ability to save his club from a relegation battle.
"I never worry about my position. I don't feel fear. You cannot be a coach if you feel it," he said.
"You have to work, take the decision and you need to show confidence to your players.
"It's not about my position, it is about Fulham's position. That is the most important thing. Obviously it is just six games, but it is true we need points."
It is four league losses in six games this season for Arbeloa, whose team have conceded after 75 minutes in matches with Sunderland, Crystal Palace, Manchester United and now Ipswich.
Although Arbeloa had a brief spell at Real last season following Xabi Alonso's sacking, the former Liverpool defender has never managed in the Premier League before.
His only managerial experience prior to Real came with the Spanish club's second team.
But the 43-year-old pointed to his impressive playing career with Real, Liverpool and Spain as proof he is equipped to handle the heart.
"Me? No, maybe you don't know me but I played for the best team in world. I have coached the best team in the world," he said.
"Maybe you don't know, but just to let you know, that pressure is part of my life since I was a kid.
"So, it is normal in football. It is normal for players, it is normal for coaches and everybody that is around a team. I think pressure is something that is important for me and I like it."