Mr Eastwood said: "Any new Government must use its power to tackle the real challenges faced by this society, it must be a new government which ends the decade long pattern of DUP intransigence and Sinn Fein weakness".
Downing Street declined to comment on Mrs Foster's remarks, insisting Mrs May had made the reason for her trip.
"We had reached an accommodation with the leadership of the DUP".
There was no breakthrough in talks to resolve Northern Ireland's 13-month power-sharing impasse on Monday, despite Irish Prime Minister Leo Varadkar and British Prime Minister Theresa May visiting Belfast to meet the territory's political leaders.
DUP leader Arlene Foster has said there is no prospect of a return to devolved government for Northern Ireland.
Yesterday, Foster said their presence had proved a "bit of a distraction" as it interrupted negotiations.
"Despite our best efforts, serious and significant gaps remain between ourselves and Sinn Fein, especially on the issue of the Irish language", she added.
The high-level meetings also included the Irish Taoiseach Leo Varadkar and his deputy Simon Coveney. She said she did not feel it necessary to meet Mr Vardakar because the negotiations were touching on matters exclusively related to internal matters within Northern Ireland.
"We will keep at it and continue to work on that progress", she said.
Officials from Dublin and Westminster will work together on efforts to avoid a hard border between the United Kingdom and Ireland after Brexit, Leo Varadkar said.
Finding a compromise resolution to the thorny language dispute that will satisfy both parties is key to breaking the Stormont deadlock.
"It is now clearer than ever that the Petition of Concern must be reformed - up front as part of any Stormont Talks deal - if the devolved institutions are to have any credibility in being able to provide a government for everyone".
However, pro-Leavers argue that remaining within the two would demean the referendum result as it would prevent the United Kingdom from striking free-trade agreements with other countries.
Alliance Party leader Naomi Long said Northern Ireland was now in "uncharted territory" and that political investment had been "swept away" over the "most minor of issues".
'However they want to describe it, the DUP know that agreement requires an Acht Gaeilge.
"The DUP need to make up their mind about whether they are up for a deal or not".