David Moyes' side came out on top in a hard-fought encounter at Goodison Park on Saturday afternoon to move within four points of the final Champions League spot
Kevin Mirallas' first-half goal secured the points at Goodison Park, as the hosts moved within four points of Chelsea in the final Champions League spot.
And, whilst Baines conceded that Everton had not been at their best against the Potters, he claimed the Toffees' resilience provided the foundations for victory.
"We knew it would be a really tough game. We’d have taken a 1-0 beforehand it’s all about winning games especially at this stage of the season," he told ESPN.
"It’s three more points that keeps us fighting. It’s very important because it keeps us within touching distance and we’ve got a very big game to look forward to next week at Spurs.
"They’ve always got that aerial threat and we got pinned back a bit in the second half and we couldn’t get our momentum going again but it is difficult when they were pushing forward but we showed some resilience and deserved the win."
David Moyes opted to employ three centre-backs against Tony Pulis' side, a tactic which Baines believes paid off handsomely.
"We got a clean sheet with three at the back so that was a positive. It was the personnel we had today we had a few really important players missing and the reshuffle worked for us," he added.
The England international also praised Mirallas for his solo goal and looked ahead to next week's crucial clash with third-placed Tottenham at White Hart Lane.
"It was just a counterattack we know Kevin has the skill and pace to run at people and he had the composure at the end of it and it was a great goal," he continued.
"It keeps us fighting and within touching distance of those teams above us and makes next week very important.
"We won’t stop believing it’s what we do here we’re off the back of a couple of good home wins if we can win all our remaining ones at Goodison and hold firm away it’ll certainly give us a chance but there’s a lot of football to play and it’s up to us to do it."