However, his vision for a more attacking style of play in the future has been dealt a blow with the board seemingly at loggerheads with manager Sam Allardyce over the future of talented but temperamental midfielder Ravel Morrison.
"There were games last season where I had tears in my eyes. It just wasn't good enough," Sullivan said in an interview with Talksport radio.
"We told the manager we want a more attacking form of football but at the same time the manager has to pick the team. It's his decision what he does."
West Ham, who finished in mid-table after fighting against relegation from the Premier League for most of last season, appear to be entering a pivotal period in their preparations for the new campaign.
Sullivan, who jointly owns the club with David Gold, wants Morrison to stay at Upton Park even though Allardyce has said he is open to selling the former Manchester United player.
"Sam has said Ravel is not part of his plans but we - as a board - see him as part of our plans," he explained.
"We would like to sit down and give him a longer contract...but we have to agree it with the manager because there's no point signing a player he's not going to play."
Sullivan believes Allardyce is willing to try to accommodate the vision for a more attacking style of play.
"We only would [consider sacking the manager] if Sam was unreceptive towards what we saw was the future in terms of attacking a bit more, bringing in new players and us being involved a bit more with the transfers," he added.
"We think what we've bought (recently) is better value for money and at least we've got some more lottery tickets that could turn into jackpots."
Among West Ham's new recruits are striker Mauro Zarate, midfielders Diego Poyet and Cheikhou Kouyate and defender Aaron Cresswell.
(Reporting by Tom Hayward, editing by Tony Jimenez)
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