Arsenal conceded a late goal to lose 0-1 at second-tier club Ipswich in the League Cup semifinals on Wednesday, and Liverpool went down 1-2 at Blackpool in the Premier League.
Tamas Priskin's goal gave Ipswich the first-leg advantage, holding off a defender before sliding the ball past goalkeeper Wojciech Szczesny in the 78th minute.
Kenny Dalglish's first Premier League match back as Liverpool manager ended in the club's second loss this season to Blackpool, which returned to the top flight after a 39-year absence.
Fernando Torres scored after three minutes, but Blackpool's Gary Taylor-Fletcher leveled nine minutes later and teammate D.J. Campbell's second-half goal inflicted Liverpool's 10th loss of the season.
Ipswich has had a turbulent week with Roy Keane leaving as manager and Paul Jewell appointed as his successor. The team is only three points above the League Championship relegation zone, and had been thrashed 7-0 at Chelsea in the FA Cup last Saturday.
"Pretty much everyone in the country wrote us off today, so we've surprised a lot of people," Ipswich captain David Norris said. "We let a lot of people down against Chelsea. We didn't do ourselves justice, so we went out tonight with that bit of extra determination.
"But there's still work to be done and we still have to go to the Emirates in the second leg."
Looking for his first trophy since the 2005 FA Cup, Arsenal manager Arsene Wenger fielded a strong side that included Spain World Cup winner Cesc Fabregas and England internationals Theo Walcott and Jack Wilshere.
But the Premier League's third-place team failed to hit top gear and was fortunate not to lose by a bigger margin ahead of the second leg at Emirates Stadium.
"Let's not think that we lost the game because we haven't bought a central defender," Wenger said. "We lost the game because we didn't play as well as we can."