During that spell they won just two of their last 10 matches but Saturday's visit of West Ham is the start of three home games in four fixtures.
Newcastle, Fulham and Middlesbrough must all travel to the Reebok Stadium, with trips to Stoke and West Brom also coming in that period.
And Basham believes because there is more expectation on the team to do well against such clubs it increases the pressure on the players.
"We've had a tough run against and played the likes of Manchester United and Arsenal - but this will be even tougher because we're playing teams around us in the league," the 20-year-old told the Bolton News.
"These are must-win games if we don't want to get relegated. West Ham are playing well at the moment and it will be a tough game, but we know what we have to do."