The Hammers' season is at risk of unraveling after they were eliminated from the FA Cup courtesy of a 4-0 humiliation at the hands of West Brom.
But Sullivan is confident the same thing will not happen again when West Ham travel to Tottenham in the Premier League next Sunday.
West Ham, for one, will have a number of key players back from injury, while the east London side have won three of their last four clashes with Spurs in all competitions (having beaten the north London club during both of their previous two visits to White Hart Lane).
"It will take a few days to get over this loss but we have to dust ourselves down as we have the fantastic opportunity of bouncing back in the big London derby with our neighbours Tottenham Hotspur on Sunday," the West Ham co-chairman said.
"We hope to have several of our injured players back and with a good recovery and preparation period I believe we can go to Tottenham with confidence that we can get a result."
Earlier this season, Spurs had the last laugh at West Ham when Eric Dier scored a late winner at Upton Park.
The Hammers will no doubt be desperate to avoid a similar outcome, although Mauricio Pochettino's men are a side in form.
Can Sullivan's words inspire his troops to stop the rot and kick West Ham back into gear against Tottenham?