During his pre-recorded radio show on XFM, which will air on Thursday (06.02.14), the musician plays Oasis hit 'Stop Crying Your Heart' and introduces the track by revealing people still think he's ''bitter'' about the two bands' rivalry during the 1990s.
He tells listeners: ''When people around me inadvertently mention something to do with Oasis, or to do with something to do with Oasis, they generally turn to me and apologise.
''So if they say: 'I remember when I bought 'Roll With It'', they go, 'Sorry Dave!' Or they say, 'I think the new Beady Eye single's quite good ... Sorry Dave!'. So clearly people think that I'm still bitter about the battle of Britpop.''
Blur were locked in a constant chart battle with Oasis in the mid-1990s, which culminated in them releasing singles in the same week in 1995, with Blur's 'Country House' topping the chart above their rivals' track 'Roll With It'.
After a huge backstage argument between frontman Liam Gallagher and his guitarist brother Noel, Oasis split in 2009 and the siblings have barely spoken since, instead deciding to focus on separate careers with Beady Eye and Noel Gallagher's High Flying Birds.
Meanwhile, Blur split in 2003 but reunited in 2008 and frontman Damon Albarn confirmed last summer that he will reunite with his bandmates - Dave, bassist Alex James and guitarist Graham Coxon - to record a new album following the release of his own solo LP this year.
Last week, The Who frontman Roger Daltrey hinted that he would like to try and get Oasis to reunite for a Teenage Cancer Trust gig next year.
He said: ''Noel and Liam are brothers so it will all be alright. Don't worry. Blood is thicker than music...
''Could I bring them together for a Teenage Cancer Trust show? Ask me next year.''