In a game of few clear-cut chances, Paul Anderson fired over after 38 minutes before Thomas Ince shot straight at City goalkeeper Tom Heaton before the break.
Steven Davies' header was ruled out before Kirk Broadfoot's 69th-minute header almost put Blackpool ahead only for a fine save by Heaton.
Thompson said: "We are trying to play a style of play that suits us but we are finding it very frustrating on that pitch.
"We are adapting and changing the way we play at home which is wrong. It's a leveller that pitch. It's frustrating for our players who want to get out and try and trust themselves with it.
"You try and play in the right areas, but the players have to sometimes take two touches instead of one. It's wrong that we've got a fantastic passing team and we're struggling to flow at Bloomfield Road.
"We've always said we can't keep relying on Ince. He's got the most goals and assists for us. But even the midfield should be setting themselves targets to get goals. They need to chip in as well as the strikers.
"What we will be looking at this week is trying to get a big target man in as well."
- Sports & Recreation
- Tom Heaton
- Kirk Broadfoot
- Steven Davies