There will likely be some significant consequences as a result of Liverpool's capitulation at the Britannia Stadium on Sunday afternoon, but the most immediate--other than humiliation, shame, sadness, three points lost, etc.--is that Brendan Rodgers' side finished the Premier League season sixth. Tottenham Hotspur edged Everton 1-0 at Goodison, giving them the fifth spot in the final table and securing passage straight into the group stages of Europe's second-tier club competition.
Southampton's loss at Manchester City meant Liverpool were spared the indignity of the seventh-place finish their performance today deserved, but finishing sixth comes with consequences of its own. Rather than start continental competition in mid-September, Liverpool are now looking at a far earlier opening fixture for the 2015-2016 season, one that could come less than a week after they wrap up their tour of Australia and Malaysia.
Third-round qualifying matches are scheduled to start on the 30th of July, with the second leg coming a week later on August 6. The first leg is just six days after the fixture currently scheduled against a Malaysian XI in Kuala Lampur, meaning there would be plenty of traveling to go along with the normal recovery and return to fitness that the preseason allows for. Liverpool would discover their opponents during the draw on July 17.
If they secure progress past the third round, Liverpool would then learn their playoff opponent on August 7 and face the last hurdle before the group stages on the 20th and 27th of August, after the Premier League season is already underway. That's at least two matches and potentially four more to add to the calendar; this season Liverpool only played three competitive fixtures before the September international break, but they could have as many as seven by the time August is over.
**Edit: This holds if Aston Villa win the FA Cup. If Arsenal win, Liverpool will enter straight into the group stages, which, as noted above, will begin in mid-September. Earlier version of this post did not identify the different outcomes depending on the FA Cup winner.**